text:
Review Request/Contact
The Wandering Wordsmith
Wandering through words.
Category: Sci fi
Review | Beyond the Dragon's Gate by Yoon Ha Lee
December 12, 2020 December 12, 2020 DeAnneLeave a comment
Former Academician Anna Kims research into AI cost her everything. Now, years later, the military has need of her expertise in order to prevent the destruction of their AI-powered fleet.
I wasn't exactly sure what I was getting into with this story, but I knew I wanted to check out some of Yoon Ha Lee's writing. I loved how we got dumped right into the middle of the story, and got little snippets of information about the ongoing conflict in the world from the main character's perspective. I would definitely read more from this specific character's view, but I did finish the story wanting a little bit more. Maybe a little more backstory, a little more fleshing out – but for a snapshot of a single concept/issue, this was a great read.
Review: Tomorrow's Wilderness Vol 1
April 1, 2020 April 1, 2020 DeAnneLeave a comment
Gengineers extraordinaire! The intrepid duo of Joy (Prof. Williams) and George (Prof. Martinez) tackle challenges ranging from invasive pyromaniac knapweed to pretty poisonous pet Puppysaurs. A lighthearted romp through the future of genetic engineering.
These stories are set in a future roughly 60 years from now (approximately 2080). All of the stories feature organisms with unusual genetics. These organisms were either created intentionally for various reasons ("Sofia's Seed Weevils", "The Great Knapweed Round-up", "Grandma's Kittens", and "Please Don't Feed the Wildlife") or were discovered in the wild ("Terroctopus Paxarbolis", "The Squirrels of Snohomish County", and "Gigantanthropus Canadensis").
In each story, George and Joy face a genetic or environmental challenge. The challenge may be invasive plants ("Sofia's Seed Weevils" and "The Great Knapweed Round-up"), identification or protection of rare or challenged species ("Terroctopus Paxarbolis", "The Squirrels of Snohomish County", and "Gigantanthropus Canadensis"), or dealing with the consequence of poorly managed genetic constructs which have escaped into the wilderness ("Grandma's Kittens", and "Please Don't Feed the Wildlife").
In each story, Joy and George are successful in resolving the issues, typically through some combination of cleverness, scientific acumen, and more than their fair share of good luck.
The stories are lighthearted and optimistic, George and Joy (and their students) have a lot of fun along the way, but nonetheless each story is grounded in real and factual challenges facing the wilderness of the future.
For the reader interested in the underlying scientific details, an Appendix is provided which clarifies the science versus the fiction in each story.
I won't lie, I was sucked in when I heard the word "puppysaurs" and was instantly intrigued by this collection. Through the stories in this collection we follow two scientists (Joy and George) as they face different genetic dilemmas. They are often called on to identify mysterious animals or flora. The banter an friendship between the two of them is one of the best things in the collection, and really carries over from story to story.
One thing to keep in mind is that there is a lot of scientific language and sometimes the explanations are very technical, so if do not enjoy that type of writing this may not appeal to you. I absolutely ate it up since it is something I enjoy, and I loved the talk about genetic splicing as well as examination of what some of the consequences of messing with genes may be.
I really enjoyed this collection and it was wonderful to follow Joy and George through their adventures. Thanks so much to the author for reaching out to me and offering me a copy of this book!
Review: The Last Conversation
January 22, 2020 January 21, 2020 DeAnneLeave a comment
What's more frightening: Not knowing who you are? Or finding out? A Bram Stoker Award–winning author explores the answer in a chilling story about identity and human consciousness.
Imagine you've woken up in an unfamiliar room with no memory of who you are, how you got there, or where you were before. All you have is the disconnected voice of an attentive caretaker. Dr. Kuhn is there to help you—physically, emotionally, and psychologically. She'll help you remember everything. She'll make sure you reclaim your lost identity. Now answer one question: Are you sure you want to?
This is the last story from the Forward collection I had left, so I was excited to get to it. Since it is so short I don't want to say much about it since it would likely be a spoiler. This was my first experience with Paul Tremblay's writing though I've heard tons of great things about it in the past so I was eager to see if I liked it. I did really enjoy the writing and the language used – plus the twist at the end was really good and surprising. The story itself speaks to a number of things regarding science, morals and the lengths that people will go to. I felt that the story could have been much longer and kinda wished it was, but I still really enjoyed it.
Review: Killer Domes and the Chosen One
As the old world burned, the elite departed to colonise space in search of a new home. Most of the human species perished on earth's surface, but a protected few remained. Many generations passed without question, but now suspicions are starting to rise.
Follow the story of Maz and her best friend Hap, as a chance encounter with a stranger lures them into a mission to decide the future of humankind.
Killer Domes and the Chosen One is not your typical start to a sci-fi adventure. In this world the Elites have left behind some people on earth, but left them within domes to protect them from the world as it burned. We primarily follow Maz, who prides herself on excelling and gaining status in the dome.
The world building itself as well as the descriptions of how things worked within the dome provided for a very strong beginning and a good foundation for the continuing story. While things seem pretty perfect and without conflict at first, this soon changes and we go on a twisting adventure that is full of surprises.
If you want a quick adventure that will make you want to continue on in the series be sure to check it out. Starting today (December 24th) this book is available for free on Kindle, but make sure to grab it as this deal only lasts three days!
Review: You Have Arrived at Your Destination
November 27, 2019 November 27, 2019 DeAnne1 Comment
Nature or nurture? Neither. Discover a bold new way to raise a child in this unsettling story of the near future by the New York Times bestselling author of A Gentleman in Moscow.
When Sam's wife first tells him about Vitek, a twenty-first-century fertility lab, he sees it as the natural next step in trying to help their future child get a "leg up" in a competitive world. But the more Sam considers the lives that his child could lead, the more he begins to question his own relationships and the choices he has made in his life.
This one was probably my least favorite of the Forward series so far, but I didn't dislike it. It certainly has a valid discussion regarding genetic manipulation and just what corporations may be doing (or may do in the future) with genetic material they receive from individuals; however, I feel it could have benefited from being a little more fleshed out and longer.
The writing was interesting and compelling, which I really enjoyed and the characters had true personalities, but the main character's decisions were sometimes not truly explained or perhaps a little unbelievable. Still, when he was talking with other characters, or talking to those at Vitek, the internal dialogue he has with himself was engaging and some of the best parts of the story.
Overall it was still a valuable premise and conversation to have and if it were a little longer and more fleshed out I think it would have had a much higher star rating.
Review: Emergency Skin
What will become of our self-destructed planet? The answer shatters all expectations in this subversive speculation from the Hugo Award–winning author of the Broken Earth trilogy.
An explorer returns to gather information from a climate-ravaged Earth that his ancestors, and others among the planet's finest, fled centuries ago. The mission comes with a warning: a graveyard world awaits him. But so do those left behind—hopeless and unbeautiful wastes of humanity who should have died out eons ago. After all this time, there's no telling how they've devolved. Steel yourself, soldier. Get in. Get out. And try not to stare.
Well this one was quite a ride! It hit really close to home considering the current state of our planet both climate wise and economically. It discusses earth and what could happen if people cared more about others and the planet then their own gain.
This story follows a 'being' who's been promised skin in exchange for a supposedly dangerous mission of going back to Earth to get something their superior society needs. What they find surprises both them and the AI that is within them to keep them in check. What follows is a tale of dual perspectives, deception and important lessons about humankind in general.
Review: Ark
On the eve of Earth's destruction, a young scientist discovers something too precious to lose, in a story of cataclysm and hope by the #1 New York Times bestselling author of the Divergent trilogy.
It's only two weeks before an asteroid turns home to dust. Though most of Earth has already been evacuated, it's Samantha's job to catalog plant samples for the survivors' unknowable journey beyond.
Preparing to stay behind and watch the world end, she makes a final human connection. As certain doom hurtles nearer, the unexpected and beautiful potential for the future begins to flower.
Ark is another installment in Amazon's Forward series where we're facing the end of earth. In this one, a asteroid is about to hit earth and destroy life as we know it. Those that are left on earth are scientists who are frantically working to catalog as much flora and fauna as they can before they leave a couple days before it hits.
Since this is a really short story I'm not going to say much about it because pretty much anything would be a spoiler, but this is an interesting perspective on the different decisions people may make if they know the world is ending. The main character we follow is Samantha, whose perspective and feelings change based on things she discovers and people she talks to.
It's a great look at what different people may do when facing the destruction of everything they know. I'm eager to read the rest of the collection and see what other stories these authors have come up with.
Review: Summer Frost
A video game developer becomes obsessed with a willful character in her new project, in a mind-bending exploration of what it means to be human by the New York Times bestselling author of Recursion.
Maxine was made to do one thing: die. Except the minor non-player character in the world Riley is building makes her own impossible decision—veering wildly off course and exploring the boundaries of the map. When the curious Riley extracts her code for closer examination, an emotional relationship develops between them. Soon Riley has all new plans for her spontaneous AI, including bringing Max into the real world. But what if Max has real-world plans of her own?
Overall I really enjoyed this novella that is an interesting spin on the trope of AI becoming too sentient and evolved and wreaking havoc while they try to take over. It's a constantly debated question as to how smart is too smart for technology.
This story follows Riley, a programmer and Max and AI that was originally an NPC in a video game that somehow changed the game and became their own entity. Riley is obsessed and constantly testing how Max can learn and just how much they can evolve. Her obsession is dangerous and drastically changes her life.
Part of me feels as if this could have been longer, but the rest of me feels it was the perfect length. It was a short, succinct tale that is cautionary in a lot of ways. Could the characters have had more backstory and development? Absolutely, but they didn't necessarily always need it.
Even though it is short, Blake Crouch's signature twists and turns are still there and there were definitely a few that kept me guessing. If you like his writing you will probably really enjoy this as well.
Review: Mercenary's Child
September 2, 2019 DeAnne2 Comments
In Mercenary's Child we mainly follow Janus, a young man from the slums of Cerberus Corporation. No one knows where he came from, as another girl in the slums, Clara, found him and raised him by herself. From the very beginning you can tell that Janus has a bit of a chip on his shoulder. He does come off as arrogant rather than just being sure of himself and pretty early on we can see this getting him into trouble. Pretty early on in the book he is sold by the higher ups of the corporation he lives in to the ODIN mercenaries.
The world building in this book is superb, though it does take up a good chunk of the book. You can really understand what has happened in this sci fi/dystopian world to get it where it is today. Once he is with ODIN, there is even more layering of the world. The usage of references to mythologies (especially Norse in the case of ODIN) was also a great touch.
A good portion of the book is also Janus and his fellow cadets training and learning the ways of ODIN, but it's a great way for them to build relationships and to figure out what each is good at. We see more of Janus being arrogant and over confident, and being warned about what such attitudes could do.
There is definite growth in Janus and his fellow cadets as they go through training and their first mission, where things far larger than them are revealed. The way the story ends, you know some things that will probably happen in the following book, but it's also a good ending that leaves the reader anticipating what will be coming.
Thanks to Vulpine Press for giving me a copy of this book. It's out now, so be sure to pick up a copy of it sounds like something you would enjoy. Happy reading!
Review: Unpopular and Unplugged
August 3, 2019 DeAnneLeave a comment
This story follows Erin Song, a girl who lives in a technology driven world and who is not popular, but is also not the most unpopular person at school. After she makes a mistake and gets in trouble, her parents ground her and take away ALL screens and technology. It's then that the story really gets started and Erin starts to realize that some weird things are going on, things that she is only aware of now that she isn't staring at screens all day.
This story was super fun and perfectly tells some great truths about technology and relationships. Through her adventure a lot of things come into focus for Erin and she realizes that some of the things that were super important to her aren't really that essential or integral to life. Through her actions she learns some lessons and gets closer to deciding what type of person she wants to be. Shout out to her grandma, who was one of my favorite characters in the story.
The art style and illustrations are full of bright colors and convey a young person's view of the world around them. It was super easy to read and understand, with humor woven in that perfectly fit the story and would definitely appeal to the audience it's targeted for.
Unplugged and Unpopular by Mat Heagerty comes out from Oni Press on October 15th, be sure to check it out!
Follow The Wandering Wordsmith on WordPress.com
Anthologies Blog Tour BookBlogtober Book Tags Can't Wait Wednesday Cover Reveal Deals discussion Fantasy Favorite Reads Giveaway graphic novel hauls Horror/Thriller Just Talk Manga middle grade NaNoWriMo Paranormal Poetry Recommendations Reviews Romance Sci fi Short Stories Supernatural TBRs Wrap Ups writing Young Adult


Listen to the new comedy song released in the market and the name of the new song is Singham by Singer Tejas Regmi & Sandhya Budha (Kauli Budhi). The Lyrics of the song is given by Tejas Regmi and the music is given by Tejas Regmi. Artists – Yadav Devkota (Sarape), Sandhya Budha (Kauli Budhi) & Sher B. D.C, Editor – Sujan Shahi, Camera – Harish Mahara, Director – Saroj Roshan Bhattarai.


text:
Author writes away the pain in debut poetry book, After the Snap
by Ark Weekender
Ark Weekender
Kian Furnace reopens wounds of heartbreak, exposes vulnerability after divorce at height of #BLM movement through rhythm and flow
Months after a bitter divorce, Kian Furnace stood on the wharf of Shockoe Bottom in Richmond, Virginia. While looking at lapping waves of water that once ushered in slave ships, he stood in an existential juxtaposition. He was fresh from a divorce, but there he stood, getting some fresh air from his friends' wedding reception at a nearby venue.
His recent history was a bitter pill. Accomplished in his career as a non-profit management and approaching midlife without children, Furnace learned through a phone call that his wife of five years was leaving him. By his own admission, he should have sought therapy, but instead he turned to the pen to write through his pain. Then he shared his work at poetry readings. In fact, he told a childhood acquaintance who also attended the Virginia festivities that he would drive to Charlotte, North Carolina that evening for a poetry slam. Poetry was his passion, but as of late, became his therapy.
Years later, after remarrying his college sweetheart, Furnace debuts, After the Snap, a book he says reveals his "emotional rollercoaster" of verses and poetry.
"Author and syndicated radio host Michael Baisden revealed that men do cry in the dark," said Furnace who now lives in Durham. "When the lights came on, I wrote my pain."
Taking readers through an amalgamation of fear, self-doubt, regret, hurt and eventually hope and healing, After the Snap is the first of a three-part anthology of poems written after, during and before "the snap" or divorce. Furnace's literary work chronicles his progress and eventual romance with his current wife.
For Furnace, the poetry collection is "how I was going to give myself therapy and track my recovery."
Since childhood, Furnace has been writing poetry. From the time I was old enough to operate my father's record player as a child in Inglewood, California, he played music that spoke to him. "I wanted to speak back so I began to write poetry."
Going through high school sharpening his poetry chops then graduating from Wilberforce University, an HBCU in Ohio, poetry always became the way he wrote the soundtrack to his life.
When the nation shuttered during a Covid-19 quarantine, he decided it was the perfect opportunity to publish his first book. Little did he know that After the Snap would also release during the height of a social justice movement affirming the lives of African Americans taking place throughout the country.
Juxtaposed against a backdrop of civil unrest, Furnace is unapologetically vulnerable about his own emotional setback, low self-esteem and grief following the breakup of his marriage.
His revelation is the essence of vulnerability in terms of stepping out of his comfort zone and exposing himself emotionally to the world as a black man rejected by the very love he vowed to honor and protect.
"It is the sometimes bitter, sometimes sweet, poetic pouring of his own reality on the written page so that you may find healing or just know that you're not alone," writes Ronda TruFiyah Lloyd Peck in the forward of After the Snap. "His writing is sentimental, mellow, powerful, yet smooth; picture Common telling poetic lullabies in between sips of the finest cognac and you will sense the velocity of this work."
While book one is an ebb and flow of choppy waters of the heart like the Shockoe Bottom waves he once looked on in grief, Furnace promises there is calm after the storm as healing leads to love again.
Buone vacanze! A glimpse at Italy's winter festivals
City of Newark goes online to auction off homes
Latest from Ark Weekender
Summertime, and the living is . . . better
Kicking off Ark Republic's "Meet Me Outside" summer theme, cabin fever reached a fever pitch, now
8 drive-in theaters to check out in the Tri-state area this summer
No longer a thing of the past, drive-in movie theaters are the new, old-school rave.
Protest art in the time of pain and rage | Photo Story
With protests comes protests art. This story captures some of the visual art that creates the
25 Museums and tours featuring Black cultural contributions
So what, Black History is over. We know that exploring the impact and contributions of Blacks
Missed Ghana's 'Year of Return'? No worries, here are 8 significant, historical sites you should visit | Photo + Story
Ghana's "Year of Return" initiative sparked a movement of Blacks and Africans in the diaspora to

redpajama_set_name: RedPajamaCommonCrawl


text:
// Licensed to the .NET Foundation under one or more agreements.
// The .NET Foundation licenses this file to you under the MIT license.
// See the LICENSE file in the project root for more information.

using System.Collections.Immutable;
using Microsoft.CodeAnalysis;
using Microsoft.CodeAnalysis.Diagnostics;

namespace TestResources.Analyzers;

[DiagnosticAnalyzer(LanguageNames.CSharp, LanguageNames.VisualBasic)]
public sealed class DoNothingSuppressor : DiagnosticSuppressor
{
    public override ImmutableArray<SuppressionDescriptor> SupportedSuppressions => ImmutableArray<SuppressionDescriptor>.Empty;

    public override void ReportSuppressions(SuppressionAnalysisContext context)
    {
    }
}

redpajama_set_name: RedPajamaGithub


Define the using influences of contract staff for IS project.
Such are frequently an unknown quantity. It is reasonable to assume that people who can make a living freelancing within exact technologies have a reasonable grip upon those technologies but that cannot be guaranteed. Moreover, contractors may not be familiar along with the methods and standards used within the organisation and there may be very many rework needed to get their work into line along with those of employed employees. Before committing to any calculates approximately, this is wise to interview any proposed contractors and to make an opinion as to whether any adjustments to the timescale may be required.
Illustrate the highlight report in project management methods. Highlight report: The Highlight Report is the ordinary report by the project manager to the Project Board.


text:
The Pizza Effect
Modern pizza toppings are commonly thought to have originated in Italy, but in fact they were developed by Italian immigrants in the United States and then exported back to Italy. Syracuse University anthropologist Agehananda Bharati calls this the "pizza effect" — the elements of a nation's culture are sometimes developed elsewhere and then reimported. Further examples:
Mexico City's Day of the Dead parade was invented for the James Bond film Spectre and then adopted by the city.
American blues music influenced English musicians in the 1960s, who then exported blues-rock to the United States.
Adapted from India's chicken tikka, chicken tikka masala became one of the most popular dishes in Britain before being re-exported to India.
Yoga became popular in India after its adoption in the West.
Salsa music originated largely among Cuban and Puerto Rican immigrants to New York in the 1920s and then spread throughout the Americas.
Teppanyaki, the Japanese style of cooking on an iron griddle, grew to prominence in America in "Japanese steakhouses."
The pizza example continues to "echo" between the Italian and American cultures: American tourists sought out "authentic" (non-American) pizza in Italy, and the Italians met the demand by creating brick-oven pizzerias. The Americans then carried these back to their own country. Stephen Jenkins of Humboldt State University writes, "Hence, Americans met their own reflection in the other and were delighted."
July 24, 2019 | Society
← House Debate
"Death" →


Harbin International Hotel , completed and opened to business in 1937, got its present name in 1978. Since the beginning it has received several Party and State leaders as well as renowned celebrities from home and abroad. Located in the city center, with convenient transportation and beautiful environment, it has been newly decorated with a total of 128 rooms including commercial standard rooms, luxurious suites. In the hotel you can find lobby bar, commercial center, shopping emporium, beauty saloon, meeting rooms, sun bar, dining rooms, the banquet hall, etc. The hotel is now under the full management of the Jinjiang International Management Co., Ltd.
I stayed here one night. Hotel is very nice in oriental style, very comfortable and convenience. I leaved hotel early morning and didn't take breakfast, that is why I can nothing say about it. I would like indicate on two moments. First of all, it was very hot in room. And second moment - none of employees don't know any word in English. Even it was very difficult to call a taxi in the airport. I would recommend to the employees to learn at least the most widespread English words.
It´s a beatiful hotel, with very friendly and nice employees. I'am satisfied staying at your hotel.


Washington, D.C. – (RealEstateRama) — When the new Congress considers upgrading the nation's crumbling infrastructure, lawmakers must do so in ways that help states and localities plan for the effects of more extreme weather and other climate change threats, according to a new analysis from the Center for American Progress.
Create State Future Funds: These are federally supported revolving loan funds that encourage innovative transportation systems, energy infrastructure, and flood protections in areas that need them the most.
Increase funding measures taken before disaster strikes to make infrastructure and communities more resilient in the face of more powerful floods, winds, fires, or hurricanes.
Reduce flood risks in communities by strengthening federal building requirements.
Protect communities from toxic pollution by accelerating Superfund site cleanup.
Create a disaster deductible that would establish a threshold states would need to meet to access aid from the Federal Emergency Management Association to encourage more forward-thinking and equitable development and land-use policies.
Read the analysis: "5 Ways the New Congress Should Support Resilient Infrastructure" by Kristina Costa and Cathleen Kelly.
For more information or to speak with an expert, contact Sam Hananel at "> or 202-478-6327.


text:
Co-Education
The practice of educating the sexes together
Co-education. — The term is now generally reserved to the practice of educating the sexes together; but even in this sense it has a variety of meanings. (a) Mere juxtaposition; this implies the use of the same buildings and equipment under the same teaching staff for the education of both sexes, but does not oblige the sexes to follow the same methods or to live under the same regimen. (b) Coordinate education; the students are taught by the same methods and the same teachers and are governed by the same general administration; but each sex has its own classes and, in the case of a university, its separate college. (c) Identical education; both sexes are taught "the same things at the same time, in the same place, by the same faculty, with the same methods and under the same regimen. This admits age and proficiency, but not sex, as a factor in classification" (Clarke, op. cit. below, p. 121). It is in this third and narrowest sense that co-education has been the subject of widespread discussion for some time past. In the United States especially the practice has grown rapidly during the last fifty years, while in European countries it has developed more slowly.
EXTENT.—Elementary Schools.—At present co-education is practically universal in the elementary grades of the public schools of the United States. It also prevails to a large extent in the elementary grades of private and denominational schools, including those which are under Catholic direction, notably the parochial schools.—Secondary Schools.—According to the Commissioner's Report for 1905-6, there were in the United States 40 public high schools for boys only, with 22,044 students, and 29 schools for girls only, with 23,203 students; while the co-educational high schools numbered 7,962 having on their rolls 283,264 boys and 394,181 girls; the difference indicated by these last figures is noteworthy. During the same year there were under private direction 304 high schools for boys only, with 22,619 students; 500 high schools for girls only, with 27,081 students; while the private co-educational schools numbered 725 with an attendance of 26,487 boys and 25,568 girls. From these statistics it appears that even in private high schools the number of boys is larger where co-education prevails than it is in schools exclusively for boys; and that the number of girls in co-educational schools is not very far below the number in schools exclusively for girls. Higher and Technical Educational Institutions.—Of 622 universities, colleges, and technological schools reporting to the United States Bureau of Education for the year ended June, 1906, there were for men only, 158; for women only, 129; for both men and women, 335. Comparison with earlier statistics shows a decided advance in co-education. In 1889-90 the women in co-educational colleges numbered 8075, in schools of technology, 707, and in colleges for women only, 1979; the men in all colleges numbered 44,926. In 1905-6 there were 31,443 women in co-educational colleges and 6653 in colleges for women only; the number of men students was 97,738.
The tendency in Europe, generally speaking, is to admit women to university courses of study, but under restrictions which vary considerably from one country to another. In Germany, women, for the most part, attend the university as "hearers", not as matriculated students. The custom in England is that women should reside in colleges of their own while receiving the benefit of university education. There is also considerable variety in the regulations concerning the granting of degrees to women. Replies to an inquiry issued by the English Department of Education in 1897, with later revision (United States Commissioner's Report for 1904, chap. xx), showed that of 112 universities on the Continent, in Great Britain, and in the British colonies, 86 made no distinction between men and women students, 6 admitted women by courtesy to lectures and examinations, 20 permitted them to attend some lectures only; of these 20 universities, 14 were German and 6 Austrian. The proportion of women students to the total enrollment in the universities of Central Europe is shown in the following table: Austria Total No. of Students, 22,749; Women,
Germany ….'Äû'Äû
Switzerland ….'Äû'Äû In England, provision for the higher education of women began with the founding of Queen's College, London (1848) and Bedford College (1849). In 1878 the University of London admitted women to examinations and degrees. The Honor degree examinations of Cambridge were opened to women (students of Girton and Newnham colleges) in 1881; some of the Oxford examinations were opened to women (students of Somerville College and Lady Margaret Hall) in 1884; the Scottish universities admitted women in 1892; the University of Durham in 1895; the University of Wales from its foundation in 1893. In Ireland, both the Royal University and Trinity College, Dublin, receive women students. It should, however, be noted that the number of women following university courses in England is still comparatively small. In 1905-6, the colleges mentioned above in connection with Oxford had in residence 136 students, and those at Cambridge, 316. On the other hand, the movement is stronger in some of the recently founded universities. Thus the institutions for women affiliated with the London University (Bedford, Halloway, Westfield, and Royal Free Hospital) in 1905-6 numbered 628 students. It may therefore be said that co-education in Europe, though it has made a beginning, is by no means so prominent a feature of the schools as it is in the United States. Its growth and effects are for this reason best studied in American institutions; and in these the historical facts are the more important inasmuch as they are said to furnish ample justification of the policy.
CAUSES.—The explanation of these facts is to be sought in a variety of conditions, some of which are naturally connected with the general development of the country while others maybe called artificial, in the sense that they are the application of theories or policies rather than direct responses to needs, or final solutions of problems. Thus it is significant that co-education has found its stronghold in the Northern, Central, and Western States of the Union which profited most by the Congressional land grants of 1787 and 1862 and by similar grants on the part of the several States. It was easy to argue, on the basis of democratic principles, that institutions supported by public funds should offer the same advantages to all citizens. From the founding of Oberlin College, Ohio (1833), which was the first institution of its class to introduce co-education (1837), the policy spread at such a rate that by 1880 more than half the colleges, and by 1900 nearly three-fourths, had adopted it. In the more conservative East segregation was the general practice until the last quarter of the nineteenth century. But the precedent established by Boston University (1869) and by Cornell (1872) was soon followed by many other Eastern institutions.
A still more powerful factor has been the public high school, which since 1850 has held an important place in the educational system. Some schools of this class, notably those in the West, were co-educational from the start; others were opened at first for boys only, but eventually they admitted girls on the same terms; this was the case in the larger cities of the East. In 1891, only 15 out of 628 leading cities of the country had separate high schools, in 1901 the number had fallen to 12. The growth of these schools coincided with the movement in favor of higher education for women. The leaders of this movement insisted on the right of women to have equal advantages with men in the line of education; they quite overlooked or disregarded the fact that equality in this case does not mean identity. But any defect in their reasoning on the subject was more than compensated for by their enthusiasm and perseverance. Their efforts, however, were in accordance with the demands made by industrial changes. The introduction of labor-saving machinery which gradually brought about the factory organization of industry, took from woman, one by one, her traditional employments in the home and compelled her to seek new occupations in fields hitherto occupied exclusively by man: hence the very natural demand for equal educational opportunities, not merely to secure the more complete development of woman's faculties, but also as a necessary means to equip her for her new position. The demand of course grew more imperative as the professions were opened to women. Once it was admitted that a woman might, for instance, take up the practice of medicine, it was quite obvious as a matter of public policy that she should receive the training given to every physician. How fully her claims have been recognized will appear from statistics given above of the growth of universities, colleges, and schools of technology since 1889.
The rapid spread of co-education aroused intense interest not only among educators but also in the mind of the public at large. The subject was discussed from every point of view, moral, medical, and economic, no less than educational. Special inquiries were sent out by school committees, State boards, and the United States Bureau of Education, with a view to obtaining statistics and expressions of opinion. Replies to these inquiries served as a basis for numerous reports, such as that of the Boston School Committee (Document 19, 1890) and that of the Commissioner of Education based on the inquiry of 1891. (See Commissioner's Report for 1900-1901, chap. xxviii.) The outcome of the discussion may be summarized as follows: (I) the tendency towards co-education as a universal policy was freely admitted by all parties; (2) considerable divergence of opinion was manifested as to the wisdom of co-education, particularly in secondary schools; (3) in many cases the issue was obscured by treating co-education as though it were synonymous with the higher education of women.
In order to set this phase of the question in a somewhat clearer light, it should be noted first of all that the reasons advanced in favor of the higher education of women, valid as they certainly are, do not of themselves require that this education shall be identical with that given to men. Passing over for the present the question whether both sexes should study the same subjects by identical methods for the same length of time, or even supposing that this question should be answered in the affirmative, one is not thereby compelled to admit that co-education is the only acceptable policy. The efficient work of those colleges which are exclusively for women tells strongly in favor of separate education. On the other hand, it should be remarked that the unification of the schools into a system does not necessarily imply co-education all the way through. While endorsing the practice in the elementary school for certain reasons and in the university for other reasons, one may consistently refuse to approve its introduction in the secondary school. A third consideration turns on the moral factor. This is, and always has been, of paramount importance in Catholic education. Whatever advantages of an intellectual sort may be claimed for the co-educational school, these must, from the Catholic point of view, be waived if they cannot be obtained without danger to morality. This view of course is shared by many non-Catholic parents and teachers, some of whom have made it the basis of their criticism of co-education. Doubtless, too, it would have counted for more in the discussion if the whole problem of moral education had received the attention bestowed in late years on everything pertaining to purely intellectual culture. Where that problem is overlooked or lightly dismissed, some of the most serious objections to co-education naturally lose their force, while too much weight is attached to some of the reasons on the opposite side.
PRACTTCE AND ATTITUDE OF CATHOLIC SCHOOLS.—As noted above co-education prevails in most of the Catholic elementary schools. That women should also share in the advantages of higher education is quite in keeping with Catholic policy. An instance of this is the authorization granted by Rome for women to follow, under requisite conditions, courses at the English universities (Decision of Propaganda, July 13, 1907). Another is furnished by such institutions as the Anna-Stift, a university school for Catholic teaching sisters founded at the University of Munster in 1899 to meet the wishes of the German bishops. Instruction is given by university professors not in the halls of the university but in the institute itself, an arrangement that is equivalent to what has been mentioned above as coordinate education. (See Engelkemper in Cath. Univ. Bulletin, May, 1908.) But in secondary schools, the Catholic policy is decidedly opposed to co-education. The high schools, academies, and colleges for boys are altogether separate from those for girls. Boys are taught by male teachers, girls by women, usually religious. Nothing in fact so strongly emphasizes the Catholic attitude in this matter as the work of various orders of men established to teach boys, and of no less various orders of women to teach girls. This is the century-old practice of the Church, and it is observed in all countries. Catholics, moreover, have followed with interest the discussions concerning co-education; and though in many other respects they have adopted in their own work the methods approved by experience in non-Catholic schools, they have not been convinced by the arguments advanced in favor of the co-educational plan.
From the viewpoint of economy co-education might seem the wiser plan; but as a matter of fact, by increasing the number of pupils in each class it throws a heavier burden on the teacher and it makes difficult if not impossible that individual instruction, the need of which is now so generally recognized. A saving that impairs the efficiency of the school is hardly desirable. The advantage also that is claimed on the score of improved discipline, is more apparent than real. While the boys probably part with some of their roughness it is by no means certain that the delicacy of feeling and the refinement of manner that are expected in girls, gain much by the association. Moreover, if there is a demand for better discipline, the right way to meet it is to train teachers more thoroughly in the art of school management. A skillful teacher will easily control a class either of boys or of girls by arousing and maintaining their interest in what is really the work of the school. On the other hand, it can do no harm to young people, especially boys, to cultivate betimes a spirit of obedience to law for its own sake, and not merely teach them to behave themselves out of deference for the opposite sex. There is no doubt a decided benefit to be gotten from social intercourse, provided this is accompanied by the proper conditions. The place for it is in the home, under the supervision of parents, who will see to it that their children have the right kind of associates, and will not leave them to the chance companionships which the mixed school affords. It has often been held that the co-educational system extends to the school the "good effects that flow from the mutual influence of mingling the sexes in the family circle"; but this contention evidently overlooks the profound difference between the home situation which associates children by natural ties of kindred, and the situation in school where these ties do not exist. And it further forgets, apparently, that the home influence itself has latterly been weakened in many ways and by various causes; how far co-education has contributed to this result is of course another question. At any rate, it avails nothing to argue that because boys and girls live together in the same family, it is more natural that they should be educated in the same classes. When appeal is taken to the "natural" order of things, the decision is plainly in favor of separate schools.
On physiological grounds, identical education presents serious difficulties. As no arrangement has been devised, and as none can be devised, to make the conditions of study exactly the same for both sexes, co-education really means that girls are subjected to a regimen intended and conducted for boys. To the physical strain which is thus imposed on them, girls as a rule are not equal; in particular they are apt to suffer from that very rivalry which is often cited as a desirable feature of the mixed school. If education is to take as its first principle conformity to nature, it must certainly make allowance for differences of organism and function. This need becomes the more imperative in proportion as the dependence of mind upon organic processes is more fully realized and turned to practical account in educational work. It then appears beyond question that from a psychological standpoint woman should have a different training from that which men receive. There is no question here as to the superiority or inferiority of either sex, nor will it profit to say that "soul has no gender". The fact is that each sex has its own mental constitution and its special capacities. To develop these is the work of education; but this does not mean that unlike natures shall be moulded into a superficial resemblance to each other. Even if it were desirable to have the finished product exactly the same in both sexes, it does not follow that this result is to be obtained by subjecting men and women to the same discipline. Educationists are agreed that the need of the developing mind is the first thing to be consulted in framing methods and in organizing the work of the school. They rightly condemn not only a system which treats the boy as though he were a man, but also any feature of method that fails to secure adaptation, even in detail, of the teaching to the present condition of the pupil's mind. Yet many of them, strangely enough, insist that the same training shall be given to boys and girls in the secondary schools, that is at a period which is chiefly characterized by the manifestation of profound mental differences between one sex and the other. The attempt now so generally made to obviate the physiological and psychological difficulties of co-education by adapting the work of the school to the capacities and requirements of girls, can evidently have but one result, and that not a desirable one, so far as boys are concerned.
It must further be pointed out on vocational grounds that, since woman's work in the world is necessarily different from man's, there should be a corresponding difference in the preparation. Here again it is singular that while the whole trend of our schools is towards specialization in view of the needs of after-life, no such consideration should be had for diversity of calling based on diversity of sex. The student is encouraged to take up as early as possible the special lines of work that fit him for his chosen career in business, in literary work, or in any of the professions; yet for the essential duties of life, widely different as these are, men and women receive an identical education. However great be the share which woman is to take in "the public expression of the ideal energies, for morality and religion, for education and social reforms, and their embodiment, not in the home, but in the public consciousness "—it still remains true that her success as a supporter of these ideal endeavors is closely bound up with the right discharge of those du-ties which are at once the lot and the privilege of her sex. Any influence that tends to make those duties less sacred to her or less attractive, is a menace to her individual perfection and may lead to far-reaching calamity. The lowering of sex tension, which is the strongest argument brought forward to support co-education from the view-point of morality, turns out on closer inspection to be a fatal objection; it proves too much. The "indifference" which it is said to produce has its consequences beyond the limit of school-life, and these if left to work out their own results would be, as they undoubtedly are in many instances antagonistic to the essential interests of family and home, and eventually of the national life as well.
The element of religious instruction, essential to Catholic schools, has a peculiar significance in the present problem. It not only gives free scope to ideal and aesthetic tendencies, but it also provides effectual safeguards against the dangers to which adolescence is exposed. As President Hall has said, "every glow of aesthetic appreciation for a great work of art, every thrill aroused by an act of sublime heroism, every pulse of religious aspiration weakens by just so much the potential energy of passion because it has found its kinetic equivalent in a higher form of expression" (Pedagogical Seminary, March, 1908). The "prophylactic value" of religious training is, from the Catholic point of view, far greater than that of the conditions which co-education involves and on which it depends for the development of character and morals. But this value of course can be got only by teaching religion with the same thoroughness and the same perfection of method that characterizes the teaching of other subjects, and in such a way as to make the duties which religion imposes on both the sexes not merely pleasing items of knowledge, but also vital elements in habit and action. (See Education; Schools.)
THOMAS E. SHIELDS


You are how your website looks like. Have a business website that is pleasing to the eye and invite more viewers. On the other hand, have a website that's a complete eye sore and you easily lose your audience. This is how crucial your website's design is. It can either make or break your online presence. No wonder, you have to ensure that you website's design is enticing.
Boost your brand. Your website is your brand's flagship online. Ensuring that it looks good and decent enough is one great way of giving people the impression that it is worth their trust. Being consistent with its design and elements such as colors and fonts is also a good means of establishing an online personality, something that would help people recall your brand.
Stand out from the rest. Your website is your face online. Having a good one is like having a pretty face that stands out even in the crowd. This way, you will get attention. People will remember you, too.
Increase your sales. Once you succeed at capturing people's attention and making them read everything posted on your site, it will already be easier for you to boost your sales. Since your online visitors are able to see what you can offer, they are more likely to make purchases.
Superb Technical Skills. The Philippines is full of talented and smart people who are committed to deliver only the best results. No wonder, our web designers are capable of coming up with great designs that are able to magnet online visitors.
Good Taste. Taste is also something that's truly important for every web designer. Having a good taste means having the ability to come up with great designs that look good. This is never an issue with Filipinos.
Excellent Customer Service. Communication between clients and designers are also another crucial component in any web designing project. It is through this that instructions are communicated in the right way. At the same time, communication allows the two parties to have a clearer understanding of the project. We, Filipinos, have excellent communication skills. We are not just good listeners; we are good English speakers, too.
Web design is something that should not be taken for granted by any business owners who is eager to boost his brand's exposure. To be able to succeed at it and have a web design that is meant to boost sales, one has to find the best agency to work with. For best results, outsource web design to the Philippines and let our talented and skilled designers do the job for you. Contact us now and let us get started with your web design project!


This brings me to a rant that I've been meaning to make for a while, whenever I see grant programs aimed at "Digital Youth," conferences targeted to "Youth Culture," or opinion pieces about the "digital generation." Even if I think that papers about how Palestinian girls use cell phones are interesting, I think more prominent and well-funded scholars should be looking seriously at computer-mediated communication in the 30-70 set, the demographic in which policy is made and power relationships in families, offices, and political structures may really be changing the most.
The one thing the tut-tut mainstream media and celebratory people associated with certain philanthropic organizations share is this single-minded focus on the young, whether as multitasking anti-social cyborgs, naive potential victims of sexual predators, totally unconscious confessional strip-tease artists, or plucky little superheroes who are taking on industrialized education and the copyright establishment. It's all about "other" rather than self.
To the credit of people like James Paul Gee, there are certainly mature individuals willing to look seriously at their own discourse practices critically, but I worry that their disciples in game studies and Internet research are sometimes too much in love with the exotic digital young.


In need of Doe Run Bail Bonds? Numerous Doe Run bail bond agents can bail you (or another person) out anytime during the day or night in Doe Run. BailBondsNetwork.com makes it easy to locate and get in touch with a licensed bail bond agent in Doe Run, Missouri. At your request, many bail bond agents will come pick you up privately. Installment payment plans are often available depending on each case.
Upon arrest anywhere in Saint Francois county, a person is usually processed at the Saint Francois county jail. To be released from Saint Francois jail, a few steps must occur, including being booked into jail and posting bail. Once the bail bond amount is decided, a bail bonds agent is sent to post the bail bond at the local jail. Now the release process begins and typically takes anywhere from one to two hours to complete. Even though cash bonds are acceptable, it is usually not commonly done due to financial limitations.


text:
<?php

class BaseZF_Framework_View_Helper_HeadScript extends Zend_View_Helper_HeadScript
{
    /**
     * Enable pack
     */
    static $_packsEnable = false;

    /**
     * Pack config
     */
    static $_packsConfig = array();

    /**
     * Src prefix to use CDN server or other host for static content
     */
    static $_prefixSrc;

    //
    // Prefix functions
    //

    private static function _addItemSrcPrefix(&$item)
    {
        // add preffix for cdn if required
        if (
            isset($item->src) &&
            isset(self::$_prefixSrc) &&
            substr_count($item->attributes['src'], 'http://') == 0
        )
        {
            $item->attributes['src'] = self::$_prefixSrc . $item->attributes['src'];
        }
    }

    public function setPrefixSrc($prefix)
    {
        self::$_prefixSrc = $prefix;

        return $this;
    }

    //
    // Pack functions
    //

    public function enablePacks($packsEnable = true)
    {
        self::$_packsEnable = $packsEnable;

        return $this;
    }

    public function setPacksConfig(array $packsConfig)
    {
        self::$_packsConfig = $packsConfig;

        return $this;
    }

    private function _getItemPack(&$item)
    {
        static $packsItems = array();

        // check item has href then no pack possible
        if (!isset($item->attributes['src'])) {
            return false;
        }

        // search pack
        foreach (self::$_packsConfig as $packPath => $items) {

            if (in_array($item->attributes['src'], $items)) {
                $matchPackPath = $packPath;
            }
        }

        // no pack found
        if (!isset($matchPackPath)) {
            return $item;
        }

        // no duplicate pack
        if (isset($packsItems[$matchPackPath])) {
            return false;
        }

        // build item pack
        $itemPack = $this->createData('text/javascript', array('src' => $matchPackPath));
        $packsItems[$matchPackPath] = &$itemPack;

        return $itemPack;
    }

    /**
     * Retrieve string representation
     *
     * @param  string|int $indent
     * @return string
     */
    public function toStringPacked($indent = null)
    {
        // escape options
        if ($this->view) {
            $useCdata = $this->view->doctype()->isXhtml() ? true : false;
        } else {
            $useCdata = $this->useCdata ? true : false;
        }
        $escapeStart = ($useCdata) ? '//<![CDATA[' : '//<!--';
        $escapeEnd   = ($useCdata) ? '//]]>'       : '//-->';

        // indent options
        $indent = (null !== $indent)
                ? $this->getWhitespace($indent)
                : $this->getIndent();

        // looking for packs
        $items = array();
        foreach ($this as $item) {
            if ($itemPack = $this->_getItemPack($item)) {
                $items[] = $this->itemToString($itemPack, $indent, $escapeStart, $escapeEnd);
            }
        }

        return implode($this->getSeparator(), $items);
    }

    /**
     * Retrieve string representation
     *
     * @param  string|int $indent
     * @return string
     */
    public function toString($indent = null)
    {
        // if static pack enable use toStringPacked instead of toString
        if (self::$_packsEnable) {
            return $this->toStringPacked($indent);
        } else {
            return parent::toString($indent);
        }
    }
}


text:
\section{Introduction}

This paper is a sequel to \cite{AFS-odd-stability}, where we proved that a general smooth curve of odd genus, canonically or bicanonically embedded,
has semistable $m^{th}$ Hilbert point for all $m\geq 2$. Here, we prove an analogous result for canonically embedded curves of even genus. Our main result
is the following.
\begin{theorem}[Main Result]\label{T:main-canonical}
Suppose $C \subset \mathbb{P} \mathrm{H}^0(C, K_{C})$ is a general smooth curve of even genus,
embedded by the complete linear system $|K_{C}|$. Then the $m^{th}$ Hilbert point of $C$ is semistable for every $m \geq 2$.
\end{theorem}
We refer to our previous paper \cite{AFS-odd-stability} for an extended discussion of the geometric motivation behind this result and its applications
 to the Hassett-Keel log minimal model program for $\overline{M}_g$, as well as
an informal description of the method of proof. As in \cite{AFS-odd-stability}, this generic stability result is obtained by proving that a very
special singular curve has semistable Hilbert points. The singular curve we used in \cite{AFS-odd-stability} was a balanced canonical ribbon of odd genus.
The singular curve that we will use here is the so called
{\em balanced double $A_{2k+1}$-curve} of even genus.

A {\em double $A_{2k+1}$-curve} is any curve obtained by gluing three copies of $\mathbb{P}^1$ along two
$A_{2k+1}$ singularities (see Figure \ref{F:double-A-curve}).
In every even genus $g=2k$, double $A_{2k+1}$-curves have
$2k-4$ moduli corresponding to the crimping of the $A_{2k+1}$-singularities, i.e., deformations that preserve the analytic type
of the singularities as well as the normalization of the curve;  we refer to \cite{fred} for a comprehensive
discussion of crimping of curve singularities.
We note that the parameter space of crimping for an $A_{2k+1}$-singularity with automorphism-free branches
has dimension $k$. However, in the case of a double $A_{2k+1}$-curve, the presence of automorphisms of the pointed $\mathbb{P}^1$'s
reduces the dimension of crimping moduli by $4$.

Among double $A_{2k+1}$-curves, there is a unique double $A_{2k+1}$-curve with a $\mathbb{G}_m$-action,
corresponding to the trivial choice of crimping data. We call
this curve the {\em balanced double $A_{2k+1}$-curve}.
Our motivation for considering double $A_{2k+1}$-curves comes from

the Hassett-Keel program for $\overline{M}_{2k}$, where we expect the $2k-4$ dimensional locus
of double $A_{2k+1}$-curves to replace the
locus in the boundary divisor $\Delta_{k}\subset \overline{M}_{2k}$ consisting
of curves $C_1\cup C_2$ such that each $C_i$ is a hyperelliptic curve of genus $k$.
Indeed, this prediction has already been verified in $g=4$ by the second author who showed that
the divisor $\Delta_2\subset \overline{M}_4$ is contracted to the point corresponding to the unique genus $4$
double $A_5$-curve in the final non-trivial log canonical model of $\overline{M}_4$ \cite{fedorchuk-genus-4}.

It is not too difficult to see that the balanced double $A_{2k+1}$-curve is trigonal,
 i.e., it lies in the closure of the locus of canonically embedded
smooth trigonal curves; see Proposition \ref{P:A-curve}.
From this observation, we obtain a slight strengthening of our Main Result:
\begin{theorem}[Stability of trigonal curves]\label{T:main-trigonal}
Suppose $C \subset \mathbb{P} \mathrm{H}^0(C, K_{C})$ is a general smooth trigonal curve of even genus,
embedded by the complete linear system $|K_{C}|$. Then the $m^{th}$ Hilbert point of $C$ is semistable for every $m \geq 2$.
\end{theorem}
This result leads to two related questions:
Is it true that all smooth trigonal curves have semistable $m^{th}$ Hilbert points for all $m \geq 2$?
Similarly, do other curves with low Clifford index have this property?
Surprisingly, the answer to both questions is no. It is not too difficult to see that the $2^{nd}$ Hilbert point
of a trigonal curve with a positive Maroni invariant is non-semistable; see \cite{fedorchuk-jensen} for a quick proof. In the
final section of this paper, we will present a heuristic which suggests that a smooth trigonal curve has a semistable $m^{th}$ Hilbert point
for $m\geq 3$. We also prove that the $m^{th}$ Hilbert point of a
smooth bielliptic curve becomes non-semistable below
a certain definite threshold value of $m$, depending on $g$. This is complemented by a proof of the semistability of a generic bielliptic curve of odd genus
for large values of $m$.

The outline of this paper is as follows. In Section \ref{S:A-curves},
we prove the basic facts about the balanced double $A_{2k+1}$-curve necessary to prove
semistability by the strategy described in \cite{AFS-odd-stability}. In Section \ref{S:bases},
we construct the monomial bases necessary to prove
semistability of the Hilbert points of the balanced double $A_{2k+1}$-curve. As a result, we obtain
a proof of Theorems \ref{T:main-canonical} and \ref{T:main-trigonal}; see Corollary \ref{C:main-trigonal}. In Section \ref{S:bielliptic},
we discuss finite Hilbert stability of trigonal curves with a positive
Maroni invariant and bielliptic curves.

We work over the field of complex numbers $\mathbb{C}$.

\section{The balanced double $A_{2k+1}$-curve}
\label{S:A-curves}
In this section, we give an explicit description of the pluricanonical linear system
 $\mathrm{H}^0(C, \omega_C^m)$ of the balanced double
$A_{2k+1}$-curve $C$. In addition, we prove the key fact
that $\mathrm{H}^0(C, \omega_C)$ is a multiplicity-free representation of $\operatorname{Aut}(C)$.
Following the strategy of \cite{AFS-odd-stability}, this allows us to prove the semistability of the
 $m^{th}$ Hilbert point of $C$ by writing down monomial bases for $\mathrm{H}^0(C, \omega_C^{m})$.
In Section \ref{S:bases}, we construct the requisite monomial bases and thus prove the semistability of
the Hilbert points of $C$.

Let us begin by giving a precise description of the balanced double $A_{2k+1}$-curve. Let $C_0, C_1, C_2$ denote three copies of
$\mathbb{P}^1$, and label the
uniformizers at 0 (resp., at $\infty$) by $s_0, s_1,s_2$ (resp., by $t_0,t_1, t_2$). Fix an integer $k\geq 2$, and let $C$ be the arithmetic genus $g=2k$ curve obtained by gluing three $\mathbb{P}^1$'s along two
$A_{2k+1}$ singularities with trivial crimping. More precisely, we impose an $A_{2k+1}$ singularity at
$(\infty \in C_0) \sim (0 \in C_1)$ by
gluing $C_0\setminus 0$ and $C_1\setminus \infty$ into an affine singular curve
\begin{equation}\label{E:gluing-1}
\spec \mathbb{C}[x,y]/(y^2-x^{2k+2})\simeq \spec \mathbb{C}[(t_0,s_1), (t_0^{k+1}, -s_1^{k+1})].
\end{equation}
Similarly, we impose an $A_{2k+1}$ singularity at $(\infty \in C_1) \sim (0 \in C_2)$
by gluing $C_1\setminus 0$ and $C_2\setminus \infty$ into
\begin{equation}\label{E:gluing-2}
\spec \mathbb{C}[x,y]/(y^2-x^{2k+2}) \simeq \spec \mathbb{C}[(t_1,s_2), (t_1^{k+1}, -s_2^{k+1})].
\end{equation}

\begin{figure}[hbt]
\begin{centering}
\begin{tikzpicture}[scale=2]
		\node  (0) at (-3.5, 3) {};
		\node  (1) at (-2.75, 3) {};
		\node  (2) at (-2.25, 3) {};
		\node  (3) at (-1.75, 2.5) {$A_{2k+1}$};
		\node  (4) at (-3.5, 2.25) {};
		\node  (4x) at (-4, 2.25) {$A_{2k+1}$};
		\node  (5) at (-2.25, 2.25) {};
		\node  (6) at (-3, 2) {};
		\node  (7) at (-4.25, 1.5) {};
		\node  (8) at (-3.5, 1.5) {};
		\node  (8c) at (-3.7, 1.5) {$C_0$};
		\node  (9) at (-3, 1.5) {};
		\node  (10) at (-2.25, 1.5) {};
		\node  (10c) at (-2.05, 1.5) {$C_2$};
		\node  (C2) at (-2.85, 2.7) {$C_1$};
		\draw [very thick, bend left=45] (1.center) to (5.center);
		\draw [very thick] (2.center) to (10.center);
		\draw [very thick,bend left=300, looseness=1.50] (4.center) to (6.center);
		\draw [very thick] (0.center) to (8.center);
		\draw [very thick,bend left=45] (4.center) to (1.center);
		\draw [very thick,bend right=315, looseness=0.75] (5.center) to (9.center);
\end{tikzpicture}\end{centering}
\vspace{-0.5pc}
\caption{Double $A_{2k+1}$-curves}\label{F:double-A-curve}
\end{figure}

 The automorphism
group of $C$ is given by $\operatorname{Aut}(C) = \mathbb{G}_m \rtimes \mathbb{Z}_2$ where
$\mathbb{Z}_2$ acts via $s_i \leftrightarrow t_{2-i}$ and
$\mathbb{G}_m = \operatorname{Spec} \mathbb{C}[\lambda, \lambda^{-1}]$ acts via
\begin{align*}
\lambda\cdot s_0 &= \lambda s_0, \\
\lambda\cdot s_1 &= \lambda^{-1}s_1, \\
\lambda\cdot s_2 &= \lambda s_2.
\end{align*}

Using the description of the dualizing sheaf on a singular curve as in \cite[Ch.IV]{serre-corps} or \cite[Ch.II.6]{barth},
we can write down a basis of $\mathrm{H}^0(C, \omega_C)$ as follows:
\begin{equation}\label{E:basis}
\begin{aligned}
x_1 &= \left(ds_0, \frac{ds_1}{s_1^2}, 0 \right)	& y_1 &=  \left(0, ds_1, \frac{ds_2}{s_2^2} \right)  \\
x_2 &= \left(s_0 ds_0, \frac{ds_1}{s_1^3}, 0 \right)& y_2 &= \left(0, s_1ds_1, \frac{ds_2}{s_2^3} \right)  \\
	& \vdots			& & \vdots \\
x_{k} &=  \left(s_0^{k-1} ds_0, \frac{ds_1}{s_1^{k+1}}, 0 \right)& y_{k} &= \left(0, s_1^{k-1}ds_1, \frac{ds_2}{s_2^{k+1}} \right)
\end{aligned}
\end{equation}

It is straightforward to generalize this description to the spaces of pluricanonical differentials.
\begin{lemma}
\label{L:pluricanonical-bases}
For $m\geq 2$, the product map $\operatorname{Sym}^m \mathrm{H}^0(C,\omega_C)\rightarrow \mathrm{H}^0(C, \omega_C^m)$ is surjective and
a basis of $\mathrm{H}^0(C, \omega_C^m)$ consists of the following $(2m-1)(2k-1)$ differentials:
\begin{align*}
\omega_0 &= \left((ds_0)^m, \frac{(ds_1)^m}{s_1^{2m}}, 0 \right)	&  \eta_0 &= \left(0, (ds_1)^m, \frac{(ds_2)^m}{s_2^{2m}} \right)  \\
\omega_1 &= \left(s_0 (ds_0)^{m}, \frac{(ds_1)^m}{s_1^{2m-1}}, 0 \right)& \eta_1 &= \left(0, s_1(ds_1)^m, \frac{(ds_2)^{m}}{s_2^{2m+1}} \right)  \\
	 \vdots			& &  \vdots \\
\omega_{m(k-1)} &= \left(s_0^{m(k-1)} (ds_0)^m, \frac{(ds_1)^m}{s_1^{m(k+1)}}, 0 \right) & \eta_{m(k-1)}&= \left(0, s_1^{m(k-1)}(ds_1)^m, \frac{(ds_2)^m}{s_2^{m(k+1)}} \right)
\end{align*
and
\begin{align*}
\chi_{-k(m-1)+1} &= \left(0, s_1^{k(m-1)-m-1} (ds_1)^m, 0 \right) \\
&\vdots \\
\chi_{i} &= \left(0, s_1^{-i-m} (ds_1)^m, 0 \right) \\
& \vdots \\
\chi_{k(m-1)-1} & = \left(0, \frac{(ds_1)^m}{s_1^{(m-1)(k+1)}}, 0 \right)
\end{align*
\end{lemma}
\begin{proof}
By Riemann-Roch formula, $h^0(C, \omega_C^m)=(2m-1)(2k-1)$. Thus, it suffices to observe that the given
$(2m-1)(2k-1)$ differentials all lie in the image of the map
$\operatorname{Sym}^m \mathrm{H}^0(C,\omega_C) \rightarrow \mathrm{H}^0(C, \omega_C^m)$. Using the basis of $\mathrm{H}^0(C,\omega_C)$ given by \eqref{E:basis},
one easily checks that the differentials $\{\omega_i\}_{i=0}^{m(k-1)}$ are precisely those arising as $m$-fold products of
$x_i$'s, the differentials $\{\eta_i\}_{i=0}^{m(k-1)}$ are those arising as $m$-fold products of $y_i$'s, and the differentials
$\{\chi_i\}_{i=-k(m-1)+1}^{k(m-1)+1}$ are those arising as mixed $m$-fold products of $x_i$'s and $y_i$'s.
\end{proof}

Next, we show that $|\omega_C|$ is a very ample linear system,
so that $C$ admits a canonical embedding, and the corresponding Hilbert points are well defined.

\begin{prop}\label{P:A-curve}
 $\omega_C$ is very ample. The complete linear system $|\omega_C|$ embeds $C$ as a curve on a balanced rational normal scroll
$$\mathbb{P}^1\times \mathbb{P}^1 \stackrel{\vert \mathcal{O}_{\mathbb{P}^1\times\mathbb{P}^1}(1, k-1)\vert}{\ensuremath{\lhook\joinrel\relbar\joinrel\relbar\joinrel\relbar\joinrel\relbar\joinrel\relbar\joinrel\relbar\joinrel\relbar\joinrel\rightarrow}} \mathbb{P}^{g-1}.$$ Moreover,
$C_0$ and $C_2$ map to $(1,0)$-curves on $\mathbb{P}^1 \times \mathbb{P}^1$, and $C_1$ maps to a $(1,k+1)$-curve. In particular, $C$ is a $(3,k+1)$ curve
on $\mathbb{P}^1\times \mathbb{P}^1$ and has a $g^1_3$ cut out by the $(0,1)$-ruling.
\end{prop}

\begin{proof}
To see that the canonical embedding of $C$ lies on a balanced rational normal scroll in $\mathbb{P}^{2k-1}$,
recall that the scroll
can be defined as the determinantal variety (see \cite[Lecture 9]{harris}):
\begin{equation}\label{E:determinantal}
\rank
 \left(\begin{array}{cccc|cccc}
x_{1} & x_{2} & \cdots & x_{k-1} & y_{k} & y_{k-1} & \cdots & y_{2} \\
 x_{2} & x_{3} & \cdots & x_{k} & y_{k-1} & y_{k-2} & \cdots & y_{1}
 \end{array}\right)\leq 1.
 \end{equation}
From our explicit description of the basis of $\mathrm{H}^0(C, \omega_C)$ given by \eqref{E:basis},
one easily sees that the differentials $x_i$'s and $y_i$'s on $C$
satisfy the determinantal description of \eqref{E:determinantal}.
Moreover,
we see that $\vert \omega_C\vert$ embeds $C_0$ and $C_2$ as degree $k-1$ rational normal curves in $\mathbb{P}^{2k-1}$
lying in the class $(1,0)$ on the scroll. Also, we see that $|\omega_C|$ embeds $C_1$ via the very ample linear
system $$\lspan\{ 1, s_1, \dots, s_1^{k-1}, s_1^{k+1}, \dots, s_1^{2k}\} \subset \vert \mathcal{O}_{\mathbb{P}^1}(2k)\vert$$ as a curve in the class $(1,k+1)$.
It follows that $|\omega_C|$ separates points and tangent vectors on each component of $C$. We now prove that $|\omega_C|$
separates points of different components and tangent vectors at the $A_{2k+1}$-singularities.
First, observe that $C_0$ and $C_2$ span different subspaces. Therefore, being $(1,0)$
curves, they must be distinct and non-intersecting. Second, $C_0$ and $C_1$ are the images of two branches of an $A_{2k+1}$-singularity and so have
contact of order at least $k+1$. However, being $(1,0)$ and $(1,k+1)$ curves on the scroll, they have order of contact at most $k+1$. It follows
that $C_0$ and $C_1$ on $S$ meet in a precisely $A_{2k+1}$-singularity. We conclude that $\vert \omega_C\vert$ is a closed embedding
at each $A_{2k+1}$-singularity.

We can also directly verify that $\vert \omega_C\vert$ separates tangent vectors at an $A_{2k+1}$ singularity of $C$,
say the one with uniformizers $s_1$ and $t_0$. The local generator of $\omega_C$ at this singularity is
\[
x_{k}=\left(-\frac{dt_0}{t_0^{k+1}}, \frac{ds_1}{s_1^{k+1}}, 0 \right).
\] We observe that on the open affine chart $\spec \mathbb{C}[(t_0, s_1), (t_0^{k+1}, -s_1^{k+1})]$ defined in Equation \eqref{E:gluing-1}
we have
$y_1=(0, s_1^{k+1}) \cdot x_{k}$ and $x_{k-1}=(t_0, s_1) \cdot x_{k}$.
Under the identification $\mathbb{C}[x,y]/(y^2-x^{2k+2})=\mathbb{C}[(t_0, s_1), (t_0^{k+1}, -s_1^{k+1})]$, we have $(t_0,s_1)=x$ and $(0,s_1^{k+1})=(x^{k+1}-y)/2$.
We conclude that sections $y_1$ and $x_{k-1}$ of $\omega_C$
span the cotangent space $(x,y)/(x,y)^2$ and thus separate tangent vectors at the singularity $x=y=0$.

\end{proof}

Finally, the following elementary observation is the key to analyzing the stability of Hilbert points of $C$.

\begin{lemma}\label{L:multiplicityfree}  $\mathrm{H}^0(C, \omega_C)$ is a multiplicity-free $\operatorname{Aut}(C)$-representation, i.e., no
irreducible $\operatorname{Aut}(C)$-representation appears more than once in the decomposition of $\mathrm{H}^0(C, \omega_C)$
into irreducibles.
\end{lemma}

\begin{proof} Consider the basis of $\mathrm{H}^0(C, \omega_C)$ given in \eqref{E:basis}.
Then $\mathbb{G}_m\subset \operatorname{Aut}(C)$ acts on $x_i$ with weight $i$ and on $y_i$ with weight $-i$. Thus $\mathrm{H}^0(C, \omega_C)$
decomposes into $g=2k$ distinct characters of $\mathbb{G}_m$.
\begin{comment}
On easily checks that the decomposition of $\mathrm{H}^0(C, \omega_C)$ into irreducible representations is given by
$$
\mathrm{H}^0(C, \omega_C)=\left(\oplus_{i=1}^{k}\mathbb{C}\{x_i+y_i\}\right) \bigoplus \left(\oplus_{i=1}^{k} \mathbb{C}\{x_i-y_i\}\right),
$$
and each of these one-dimensional representations is given by a distinct character of $\mathbb{G}_m \rtimes \mathbb{Z}_2$.
\end{comment}
\end{proof}

\section{Monomial bases and semistability}
\label{S:bases}
Since $\mathrm{H}^0(C,\omega_C)$ is a multiplicity-free representation of $\mathbb{G}_m \subset \operatorname{Aut}(C)$
by Lemma \ref{L:multiplicityfree}, we can apply the Kempf-Morrison Criterion
\cite[Proposition 2.3]{AFS-odd-stability} to prove semistability of $C$.
Namely, to prove that the $m^{th}$ Hilbert point of the canonically
embedded balanced double $A_{2k+1}$-curve $C$ is semistable, it suffices to check that
for every one-parameter subgroup
$\rho\co \mathbb{G}_m \rightarrow \operatorname{SL}(g)$ acting diagonally on the basis
$\{x_1, \ldots, x_{k}, y_1, \ldots, y_{k}\}$ with integer weights $\lambda_1, \ldots, \lambda_{k}, \nu_1, \ldots, \nu_{k}$,
there exists a monomial basis for $\mathrm{H}^0(C, \omega_C^m)$ of non-positive $\rho$-weight.
Explicitly, this means that we must exhibit a set $\mathcal{B}$ of $(2m-1)(2k-1)$
degree $m$ monomials in the variables $\{x_i,y_i\}_{i=1}^{k}$
with the properties that:
\begin{enumerate}
\item $\mathcal{B}$ maps to a basis of $\mathrm{H}^0(C, \omega_C^m)$
via $\operatorname{Sym}^m \mathrm{H}^0(C,\omega_C) \rightarrow \mathrm{H}^0(C, \omega_C^m)$.
\item $\mathcal{B}$ has non-positive $\rho$-weight, i.e., if $\mathcal{B}=\{m_i\}_{i=1}^{(2m-1)(2k-1)}$, and
$m_i=\prod_{j=1}^{k}x_j^{a_{ij}}y_j^{b_{ij}}$, then
\[
\sum_{i=1}^{(2m-1)(2k-1)} \sum_{j=1}^k (a_{ij}\lambda_j+b_{ij}\nu_j) \leq 0.
\]
\end{enumerate}

\begin{theorem}\label{T:ribbon}
If $C \subset \mathbb{P} \mathrm{H}^0(C, \omega_C)$ is a canonically embedded balanced double $A_{2k+1}$-curve, then the Hilbert points $[C]_m$ are semistable for all $m \geq 2$.
\end{theorem}
As an immediate corollary of this result, we obtain a proof of Theorem \ref{T:main-trigonal} and hence of Theorem \ref{T:main-canonical}:
\begin{corollary}[Theorem \ref{T:main-trigonal}]\label{C:main-trigonal}
A general smooth trigonal curve of genus $g=2k$
embedded by the complete canonical linear system has a semistable $m^{th}$ Hilbert point for every $m \geq 2$.
\end{corollary}
\begin{proof}[Proof of Corollary]
By Proposition \ref{P:A-curve} the canonical embedding of the balanced double $A_{2k+1}$-curve $C$ lies on a balanced surface scroll in $\mathbb{P}^{2k-1}$
in the divisor class $(3, k+1)$.
It follows that $C$ deforms flatly to a smooth curve in the class $(3, k+1)$ on the scroll. Such a curve is a smooth trigonal canonically embedded curve.
The semistability of a general deformation of $C$ follows from the openness of semistable locus.
\end{proof}
\begin{proof}[Proof of Theorem \ref{T:ribbon}]
Recall from Lemma \ref{L:pluricanonical-bases} that
\[
\mathrm{H}^0(C,\omega_C^m)=\lspan \{ \omega_i \}_{i=0}^{m(k-1)}\oplus \lspan\{\eta_i \}_{i=0}^{m(k-1)}\oplus\lspan \{\chi_i\}_{i=-k(m-1)+1}^{k(m-1)-1}.
\]
Now, given a one-parameter subgroup $\rho$ as above, we will construct the requisite monomial basis $\mathcal{B}$ as a union
$$
\mathcal{B}=\mathcal{B}_{\omega} \cup \mathcal{B}_{\eta} \cup \mathcal{B}_{\chi},
$$
where $\mathcal{B}_{\omega}, \mathcal{B}_{\eta}$, and $\mathcal{B}_{\chi}$ are collections of degree
$m$ monomials which map onto the bases of the subspaces spanned by
$\{\omega_i\}_{i=0}^{m(k-1)}, \{\eta_i\}_{i=0}^{m(k-1)}$ and $\{\chi_i\}_{i=-k(m-1)+1}^{k(m-1)-1}$, respectively.

To construct $\mathcal{B}_{\omega}$ and $\mathcal{B}_{\eta}$, we use Kempf's
proof of the stability of Hilbert points of a rational normal curve.
More precisely, consider the component $C_0$ of $C$ with the uniformizer $s_0$ at $0\in C_0$.
Evidently, $\omega_{C}|_{C_0} \simeq \mathcal{O}_{\mathbb{P}^1}(k-1)$. The restriction map
$\mathrm{H}^0(C, \omega_C) \rightarrow \mathrm{H}^0(\mathbb{P}^1, \mathcal{O}_{\mathbb{P}^1}(k-1))$ identifies $\{x_i\}_{i=1}^{k}$ with a basis of
$\mathrm{H}^0(\mathbb{P}^1, \mathcal{O}_{\mathbb{P}^1}(k-1))$ given by $\{1,s_0,\dots, s_0^{k-1}\}$. Under this identification, the subspace $\lspan\{\omega_i\}_{i=0}^{m(k-1)}$ is identified with
$\mathrm{H}^0(\mathbb{P}^1, \mathcal{O}_{\mathbb{P}^1}(m(k-1)))$.
Set $\lambda=\sum_{i=1}^k \lambda_i/k$. Given a one-parameter subgroup $\widetilde{\rho}\co \mathbb{G}_m \rightarrow \operatorname{SL}(k)$ acting
on $(x_1,\dots, x_k)$ diagonally with weights $(\lambda_1-\lambda, \dots, \lambda_k-\lambda)$, Kempf's result on the semistability of a rational normal
curve in $\mathbb{P}^{k-1}$ \cite[Corollary 5.3]{kempf},
implies the existence of a monomial basis $\mathcal{B}_\omega$ of $\mathrm{H}^0(\mathbb{P}^1, \mathcal{O}_{\mathbb{P}^1}(m(k-1)))$ with non-positive $\widetilde{\rho}$-weight.
Under the above identification, $\mathcal{B}_{\omega}$ is a monomial basis of $\lspan\{\omega_i\}_{i=0}^{m(k-1)}$ of $\rho$-weight
at most $m(m(k-1)+1)\lambda$. Similarly, if $\nu=\sum_{i=1}^k\nu_i/k$, we deduce the existence
of a monomial basis $\mathcal{B}_{\eta}$ of  $\lspan\{\eta_i \}_{i=0}^{m(k-1)}$ whose $\rho$-weight is at most $m(m(k-1)+1)\nu$.
Since $\lambda+\nu=0$, it follows that the total $\rho$-weight of $\mathcal{B}_{\omega} \cup \mathcal{B}_{\eta}$ is non-positive.

Thus, to construct a monomial basis $\mathcal{B}$ of non-positive $\rho$-weight, it remains to construct a monomial basis $\mathcal{B}_{\chi}$ of non-positive $\rho$-weight
for the subspace $$\lspan\{\chi_i\}_{i=-k(m-1)-1}^{k(m-1)-1} \subset \mathrm{H}^0(C, \omega_C^m).$$
In Lemma \ref{L:basis}, proved below, we show the existence of such a basis. Thus, we obtain the desired monomial basis $\mathcal{B}$ and finish the proof.
\end{proof}

Note that if we define the {\em weighted degree} by $\deg(x_i)=i$ and $\deg(y_i)=-i$, then a set $\mathcal{B}_{\chi}$ of $2k(m-1)-1$ degree $m$ monomials in $\{x_1,\ldots, x_k, $ $y_1, \ldots, y_k\}$ maps to a basis of $\lspan\{\chi\}_{i=k(m-1)-1}^{k(m-1)+1}$ if and only if it satisfies the following two conditions:
\begin{enumerate}
\item Each monomial has both $x_i$ and $y_i$ terms,
\item Each weighted degree from $(m-1)k-1$ to $-(m-1)k+1$ occurs exactly once.
\end{enumerate}
We call such a set of monomials a {\em $\chi$-basis}. The following combinatorial lemma completes the proof of Theorem \ref{T:ribbon}.
\begin{lemma}\label{L:basis}
Suppose $\rho\co \mathbb{G}_m\rightarrow \operatorname{SL}(2k)$ is a one-parameter subgroup which
acts on $\{x_1, \ldots, x_{k}, y_1, \ldots, y_{k}\}$ diagonally with integer weights $\lambda_1, \ldots, \lambda_{k}, \nu_1, \ldots, \nu_{k}$
satisfying $\sum_{i=1}^k (\lambda_i+\nu_i)=0$. Then there exists a $\chi$-basis with non-positive $\rho$-weight.
\end{lemma}

\begin{proof}[Proof of Lemma \ref{L:basis} for $m=2$]

Take the first $\chi$-basis to be
\begin{multline*}
\mathcal{B}_1:=\{ x_{k}y_1, x_{k-1}y_1, x_{k-1}y_2, x_{k-2}y_2, x_{k-2}y_3, \dots \\ \dots, x_{i}y_{k-i}, x_{i}y_{k-i-1},
\dots, x_2y_{k-1}, x_1y_{k-1}, x_1y_{k}\}
\end{multline*}
In this basis, all variables except $x_k$ and $y_k$ occur twice and $x_k$, $y_k$ occur once each. Thus
$$w_{\rho}(\mathcal{B}_1)=2(\lambda_1+\cdots+\lambda_{k-1})+2(\nu_1+\cdots+\nu_{k-1})+\lambda_k+\nu_k=-(\lambda_k+\nu_k).$$
Take the second $\chi$-basis to be
\begin{align*}
\mathcal{B}_2:=\{ x_{k}y_1, x_{k}y_2, \dots, x_ky_i, \dots,x_{k}y_{k}, x_{k-1}y_{k}, x_{k-2}y_{k}, \dots, x_iy_k, \dots, x_1y_{k}\}.
\end{align*}
We have
$$w_{\rho}(\mathcal{B}_2)=(k-1)(\lambda_k+\nu_k).$$\\
For any one-parameter subgroup $\rho$, we must have either $\lambda_k+\nu_k \geq 0$ or $\lambda_k +\nu_k \leq 0$. Thus, either $\mathcal{B}_1$ or $\mathcal{B}_2$ gives a $\chi$-basis of non-positive weight.
\end{proof}

\begin{proof}[Proof of Lemma \ref{L:basis} for $m\geq 3$]
We will prove the Lemma by exhibiting one collection of $\chi$-bases whose $\rho$-weights sum to a positive multiple of $\lambda_k +\nu_k$ and a collection of $\chi$-bases whose $\rho$-weights sum to a negative multiple of $\lambda_k+\nu_k$. Since, for any given one-parameter subgroup $\rho$,  we have either $\lambda_k+\nu_k \geq 0$ or $\lambda_k +\nu_k \leq 0$, it follows at once that one of our $\chi$-bases must have non-positive weight. We begin by writing down $\chi$-bases maximizing the occurrences of $x_k$ and $y_k$ while balancing the occurrences of the other variables.
Define $T_1$ as the set of degree $m$ monomials of the ideal
\begin{multline*}
x_{k}^{m-1}(y_1,\dots, y_{k-1}, y_{k}) + x_{k}^{m-2}y_{k} (y_1,\dots, y_{k-1}, y_{k}, x_1,\dots,x_{k-1})+\cdots \\
+x_{k}y_k^{m-2}(y_1,\dots, y_{k-1}, y_{k}, x_1,\dots, x_{k-1}) +  y_{k}^{m-1}(x_1,\dots, x_{k-1}).
\end{multline*}
The $\rho$-weight of $T_1$ is
{\small
$$\left(k(m-1)+(2k-1)\binom{m-1}{2}\right)(\lambda_k+\nu_k) + (m-1)(\lambda_1+\nu_1+ \cdots+\lambda_{k-1}+\nu_{k-1}).$$
}
Note that $T_1$ misses only the weighted degrees $$k(m-3), k(m-5), \dots,-k(m-5),-k(m-3).$$  For each $s=1, \dots, k-1$, define
$$\begin{aligned}
T_2(s) &: = \{x_{k}^{m-3}y_{k} (x_{k-s}x_{s}), x_{k}^{m-4}y_{k}^2 (x_{k-s}x_{s}), \dots, y_{k}^{m-2}(x_{k-s}x_{s})\}\\
T'_2(s) &:= \{y_{k}^{m-3}x_{k} (y_{k-s}y_{s}), y_{k}^{m-4}x_{k}^2 (y_{k-s}y_{s}), \dots, x_{k}^{m-2}(y_{k-s}y_{s})\}
\end{aligned}$$
For each $s$, the sets $T_1 \cup T_2(s)$ and $T_1 \cup T'_2(s)$ are $\chi$-bases. Using the relation $\sum_{i=1}^{k}(\lambda_i +\nu_i)=0$, one sees at once that the sum
of the $\rho$-weights of such bases, as
$s$ ranges from $1$ to $k-1$, is a {\em positive multiple} of $(\lambda_k+\nu_k)$.

We now write down bases minimizing the occurrences of $x_k$ and $y_k$.
We handle the case when $k$ is even and odd separately.

\subsubsection*{Case of even $k$:} If $k=2\ell$, we define the following set of monomials where the weighted degrees range from  $k(m-1)-1$ to $m$:
\begin{equation*}
S_1 := \left\{
\begin{array}{l}   \left.
\begin{aligned}
&x_{k}^{m-1}y_1, && x_{k}^{m-2}x_{k-1}y_1,& &\dots,&& x_{k-1}^{m-1}y_1, \\
&x_{k-1}^{m-1}y_2, && x_{k-1}^{m-2}x_{k-2}y_2,& &\dots,&& x_{k-2}^{m-1}y_2, \\
&& \vdots \\
&x_{\ell+2}^{m-1}y_{\ell-1}&& x_{\ell+2}^{m-2}x_{\ell+1}y_{\ell-1},& &\dots,&& x_{\ell+1}^{m-1}y_{\ell-1}
\end{aligned}\right\} \begin{array}{l} \text{$m$ terms in } \\ \text{each of the} \\ \text{($\ell-1$) rows} \end{array}
 \\
 \\
 \left.\begin{aligned}
&x_{\ell+1}^{m-1}y_{\ell},&& x_{\ell+1}^{m-2}x_{\ell}y_{\ell}, &&\dots, &&x_{\ell+1}^{2}x_{\ell}^{m-3}y_{\ell}, \\
&x_{\ell}^{m-1}y_{\ell-1},&& x_{\ell}^{m-2}x_{\ell-1}y_{\ell-1}, &&\dots,&& x_{\ell}^{2}x_{\ell-1}^{m-3}y_{\ell-1}, \\
&&\vdots  \\
&x_{2}^{m-1}y_1,&& x_{2}^{m-2}x_1y_1, &&\dots, &&x_{2}^{2}x_{1}^{m-3}y_1
\end{aligned}\right\} \begin{array}{l} \text{$(m-2)$ terms}\\ \text{in each of the} \\ \text{$\ell$ rows} \end{array}
\end{array}
\right.
\end{equation*}
Let $\iota$ be the involution of the set $\{  x_i, y_i \}_{i=1}^k$ exchanging $x_i$ and $y_i$.
In the set $S_1 \cup \iota(S_1)$, the variables $x_k$ and $y_k$ occur $(m^2-m)-\binom{m}{2}$ times,
$x_{\ell+1}$ and $y_{\ell+1}$ occur $(m^2-m)-1$ times, $x_{\ell}$ and $y_{\ell}$ occur $(m^2-m)-m$ times,
and $x_1$ and $y_1$ occur $m^2-m-(\binom{m}{2}-1)$ times while all of the other variables occur $m^2-m$ times. To complete $S_1 \cup \iota(S_1)$ to a $\chi$-basis, we define, for each $s=1, \ldots, k-1$, the following set of monomials where the weighted degrees
range from $m-1$ to $1-m$:
\begin{equation*}
S_2(s):= \left\{
\begin{aligned}
&x_{\ell+1}y_{\ell}x_1^{m-2} \\
&x_{\ell}y_{\ell}(x_sy_s)^ix_1^{m-2i-2},  &&\quad \text{for $0\leq 2i \leq m-2$}, \\
&x_{\ell}y_{\ell}(x_sy_s)^{i}y_1^{m-2i-2},  &&\quad \text{for $0\leq 2i < m-2$},  \\
&(x_{k}y_{s}y_{k-s})(x_sy_s)^ix_1^{m-2i-3},  &&\quad \text{for $0\leq 2i \leq m-3$}, \\
&(x_{k}y_{s}y_{k-s})(x_sy_s)^iy_1^{m-2i-3},  &&\quad \text{for $0\leq 2i < m-3$}, \\
&y_{\ell+1}x_\ell y_{1}^{m-2}.
\end{aligned}
 \right\}
\end{equation*}
For each $s = 1, \ldots, k-1$, the sets $S_1 \cup \iota(S_1) \cup S_2(s)$ and $S_1 \cup \iota(S_1) \cup \iota(S_2(s))$ are
$\chi$-bases.
We compute that in the union
\begin{equation*}
\bigcup_{s=1}^k \left(S_1 \cup \iota(S_1) \cup S_2(s)\right) \cup \left(S_1 \cup \iota(S_1) \cup \iota(S_2(s))\right)
\end{equation*}
of $2(k-1)$ $\chi$-bases the variables $x_k$ and $y_k$ each occurs
$$2(k-1)(m^2-m)-(k-1)(m^2-2m+2)$$
times while all of the other variables occur
$$2(k-1)(m^2-m)+(m-2)(m-1)$$ times.

Using the relation $\sum_{i=1}^{k}(\lambda_i +\nu_i)=0$, we conclude that the sum of the $\rho$-weights of all such $\chi$-bases is a {\em negative multiple} of
$(\lambda_k + \nu_k)$.

\subsubsection*{Case of odd $k$:} If $k=2\ell+1$ is odd, $\chi$-bases of non-positive $\rho$-weight can be constructed analogously to the case when $k$ is even.
For the reader's convenience, we spell out the details.
We define of the following set of monomials where the weighted degrees range from  $k(m-1)-1$ to $m-1$:
\begin{equation*}
S_1 := \left\{
\begin{array}{l}   \left.
\begin{aligned}
&x_{k}^{m-1}y_1, && x_{k}^{m-2}x_{k-1}y_1,& &\dots,&& x_{k-1}^{m-1}y_1, \\
&& \vdots \\
&x_{\ell+3}^{m-1}y_{\ell-1}&& x_{\ell+3}^{m-2}x_{\ell+2}y_{\ell-1},& &\dots,&& x_{\ell+2}^{m-1}y_{\ell-1}
\end{aligned}\right\} \begin{array}{l} \text{$m$ terms in} \\ \text{each of the} \\ \text{($\ell-1$) rows} \end{array}
 \\
 \\
 \left.\begin{aligned}
&x_{\ell+2}^{m-1}y_{\ell},&& x_{\ell+2}^{m-2}x_{\ell+1}y_{\ell}, &&\dots, &&x_{\ell+2}^{2}x_{\ell+1}^{m-3}y_{\ell}, \\
&x_{\ell+1}^{m-2}y_{\ell-1},&& x_{\ell+1}^{m-1}x_{\ell}y_{\ell}, &&\dots,&& x_{\ell+1}^{2}x_{\ell}^{m-3}y_{\ell-1}, \\
&&\vdots  \\
&x_{3}^{m-1}y_1,&& x_{3}^{m-2}x_2y_1, &&\dots, &&x_{3}^{2}x_{2}^{m-3}y_1
\end{aligned}\right\} \begin{array}{l} \text{$(m-2)$ terms}  \\ \text{in each of the} \\ \text{$\ell$ rows} \end{array}
 \\
 \\
 \begin{aligned}
x_{\ell+2}y_{\ell}x_2^{m-2}, \\
\end{aligned}
\\
 \\
 \begin{aligned}
x_{\ell+1}y_{\ell}x_2^{m-2}, x_{\ell+1}y_{\ell}x_2^{m-3}x_1, \ldots, x_{\ell+1}y_{\ell}x_2 x_1^{m-3}, x_{\ell+1}y_{\ell}x_1^{m-2}
\end{aligned}

\end{array}
\right.
\end{equation*}
Let $\iota$ be the involution exchanging $x_i$ and $y_i$.
In the set of monomials $S_1 \cup \iota(S_1)$, the variables $x_k$ and $y_k$ occur $\binom{m}{2}$ times, $x_{\ell+1}$ and $y_{\ell+1}$ occur $m^2-m-(m-1)$ times,
and $x_1$ and $y_1$ occur $m^2-m - \binom{m-1}{2}$ times, while all of the other variables occur $m^2-m$ times.  Finally, for each $s=1, \ldots, k-1$, we define the following set of monomials where the weighted degrees range from $m-2$ to $2-m$:
\begin{equation*}
S_2(s):= \left\{
\begin{aligned}
&x_{\ell+1}y_{\ell+1}(x_sy_s)^ix_1^{m-2-2i}, &&\quad \text{for $0\leq 2i \leq m-2$}, \\
&x_{\ell+1}y_{\ell+1}(x_sy_s)^iy_1^{m-2-2i}, &&\quad \text{for $0\leq 2i < m-2$}, \\
&(x_k y_s y_{k-s})(x_sy_s)^ix_1^{m-3-2i}, &&\quad \text{for $0\leq 2i \leq m-3$}, \\
&(x_k y_s y_{k-s})(x_sy_s)^iy_1^{m-3-2i}, &&\quad \text{for $0\leq 2i < m-3$}
\end{aligned}
\right\}
\end{equation*}
For each $s=1,\dots, k-1$, the sets
$S_1 \cup \iota(S_1)\cup S_2(s)$ and $S_1 \cup \iota(S_1) \cup \iota(S_2(s))$ are $\chi$-bases.
We compute that in the union
\begin{equation*}
\bigcup_{s=1}^k \left(S_1 \cup \iota(S_1) \cup S_2(s)\right) \cup \left(S_1 \cup \iota(S_1) \cup \iota(S_2(s))\right)
\end{equation*}
of $2(k-1)$ $\chi$-bases the variables $x_k$ and $y_k$ each occurs
$$2(k-1)\binom{m}{2}+2(k-1)(m-2)$$
times while all of the other variables occur
$$2(k-1)(m^2-m)+(m-2)(m-1)$$ times.

Using the relation $\sum_{i=1}^{k}(\lambda_i +\nu_i)=0$, we conclude that
the total $\rho$-weight of these
$\chi$-bases is a {\em negative multiple} of $(\lambda_k + \nu_k)$ and we're done.
\end{proof}

\section{Non-semistability results}
\label{S:bielliptic}

The generic semistability results of Theorem \ref{T:main-canonical} and \cite[Theorem 1.2]{AFS-odd-stability}
raise a natural question of whether Hilbert points of
smooth canonically embedded curves can at all be non-semistable. An indirect way to see that the answer is affirmative is as follows.
Denote by $\overline{H}_{g,1}^{\, m}$ the closure of the locus of $m^{th}$ Hilbert points of smooth canonical curves. Next, it is proved in \cite[Section 5]{hassett-hyeon_flip} that an application of
Grothendieck-Riemann-Roch formula allows to write
the polarization on the GIT quotient $\overline{H}_{g,1}^{\, m}/\hspace{-0.25pc}/ \operatorname{SL}(g)$ as a linear combination
\begin{multline}\label{E:polarization}
(m(m-1)(4g+2)-(m-1)(g-1)+1)\lambda-\frac{gm(m-1)}{2}\delta \\ \sim \left[8+\frac{4}{g}-\frac{2(g-1)}{gm}+\frac{2}{gm(m-1)}\right]\lambda-\delta
\end{multline}
of a tautological divisor $\lambda$ (the first Chern class of the Hodge bundle) and the boundary divisor $\delta$ (at least on the locus parameterizing curves with mild singularities).
By generalizing the proof of \cite[Proposition 4.3]{CH},
it is not too difficult to see that if $B\rightarrow \Mg{g}$ is a family of stable curves whose general fiber is canonically embedded and the slope $(\delta\cdot B)/(\lambda\cdot B)$
is greater than $(8+\frac{4}{g})-\frac{2(g-1)}{gm}+\frac{2}{gm(m-1)}$,
then every curve in $B$ (with a well-defined $m^{th}$ Hilbert point)
must have a non-semistable $m^{th}$ Hilbert point.

Two observations now lead to a candidate for a non-semistable canonically embedded curve. The first is that
$(8+\frac{4}{g})-\frac{2(g-1)}{gm}+\frac{2}{gm(m-1)}\leq 8$ for $g\geq 2m+1+1/(m-1)$. The second is that there are families
of bielliptic curves of slope $8$ (such can be constructed by taking a double cover of a trivial family of elliptic curves).
In the following result, we establish that bielliptic curves indeed become non-semistable
for small values of $m$, and show that generic bielliptic curves are semistable for $m$ large enough.

\begin{theorem}
A smooth bielliptic curve of genus $g$ has non-semistable
$m^{th}$ Hilbert point for all $m \leq (g-3)/2$. A general bielliptic curve of odd genus $g=2k+1$ has
semistable $m^{th}$ Hilbert point for $m\geq (g-1)/2$.
\end{theorem}
\begin{proof}
Let $C$ be a bielliptic canonical curve. Then $C$ is a quadric section of a projective cone over an elliptic curve $E\subset \mathbb{P}^{g-2}$
embedded by a complete linear system of degree $g-1$. Choose projective coordinates $[x_0:\ldots: x_{g-1}]$.
Suppose that the vertex of the cone has coordinates $[0:0:\ldots:0:1]$.
Let $\rho$ be the one-parameter subgroup of $\operatorname{SL}(g)$ acting with weights $(-1,-1,\dots, -1, g-1)$.
There are
\[
s_m:=h^0(\mathbb{P}^{g-2}, \mathcal{O}_{\mathbb{P}^{g-2}}(m))-h^0(E,\mathcal{O}_E(m))=\binom{g-2+m}{m}-m(g-1)
\] degree $m$ hypersurfaces containing $E$.
Thus $$\dim \mathrm{H}^0(C,\mathcal{I}_C(m)) \cap (x_0,x_2,\dots,x_{g-2})^m=s_m$$
and so there are at most
$$h^0(C,\mathcal{O}_C(m))-s_m=m(g-1)$$ elements in $\mathrm{H}^0(C,\mathcal{O}_C(m))$ of $\rho$-weight $(-m)$. The remaining $(m-1)(g-1)$ elements in $\mathrm{H}^0(C,\mathcal{O}_C(m))$
have $\rho$-weight at least $g-m$. Thus the $\rho$-weight of any monomial basis of $\mathrm{H}^0(C,\mathcal{O}_C(m))$ is at least
\begin{equation}\label{E:bielliptic-weight}
(m-1)(g-1)(g-m)-m(m(g-1)
=(g-1)((g+1)m-2m^2-g).
\end{equation}
If $m\leq (g-3)/2$, then \eqref{E:bielliptic-weight} is positive, and so $C$ has a non-semistable $m^{th}$ Hilbert point.

To prove the generic semistability of bielliptic curves in the range $m\geq (g-1)/2$, we recall \cite[Theorem 4.12]{AFS-odd-stability}
which shows that the odd genus $g$ canonically embedded rosary has a semistable $m^{th}$ Hilbert point if and only if $g\leq 2m+1$.
It remains to observe that the canonically embedded rosary deforms to a canonically embedded smooth bielliptic curve in the Hilbert scheme
of canonically embedded curves. This is accomplished in Lemma \ref{L:rosary} below.
\end{proof}

\begin{lemma}
\label{L:rosary}
The canonically embedded rosary
deforms flatly to a canonically embedded bielliptic curve.
\end{lemma}
\begin{proof} Let $C$ be
the rosary of genus $g=2k+1$ introduced by Hassett and Hyeon \cite[Section 8.1]{hassett-hyeon_flip}.
We use the notation of \cite[Section 3.2]{AFS-odd-stability}.

Consider $\mathbb{P}^{g-2}$ with projective coordinates $[x_0:\ldots:x_{g-2}]$ and define $E\subset\mathbb{P}^{g-2}$ to be the union of $g-1$ lines $L_i : \{x_{i+1}=\dots=x_{i+g-3}=0\}$,
for $i=0,\dots, g-2$
(we use the convention that $x_{i+g-1}=x_{i}$). Then $E$ is a nodal curve of arithmetic genus $1$. Since $\mathrm{H}^1(C,\mathcal{O}_C(1))=0$, we can deform $E$ in a flat family
to a smooth elliptic curve by \cite[p.83]{Kol}. Using the basis $(\eta, \omega_0, \dots, \omega_{g-2})$
of $\mathrm{H}^0(C,\omega_C)$ described in \cite[Lemma 3.6]{AFS-odd-stability},
we observe that the rosary $C$ is cut out by the quadric
$$y^2=x_0x_1+x_1x_2+\cdots+x_{g-2}x_0$$
on the projective cone over $E$ in $\mathbb{P}^{g-1}$.  Since $E$ deforms to a smooth elliptic curve, it follows that $C$ deforms to a smooth bielliptic curve.
\end{proof}

\begin{remark}[Trigonal curves of higher Maroni invariant] Theorem \ref{T:main-trigonal} shows that the general trigonal curve with Maroni invariant $0$ has a semistable $m^{th}$ Hilbert point for all $m\geq 2$.
In joint work of the second author with Jensen, it is shown that every trigonal curve with Maroni invariant $0$ has a semistable $2^{nd}$ Hilbert point and every trigonal
curve with a positive Maroni invariant has a non-semistable $2^{nd}$ Hilbert point \cite{fedorchuk-jensen}. In view of the asymptotic stability of the canonically embedded
curves \cite{mumford-stability}, this result suggests that {\em every} smooth trigonal curve of Maroni invariant $0$ has a semistable $m^{th}$ Hilbert
point for every $m\geq 2$. One also expects that for a general smooth trigonal curve of positive Maroni invariant
already the third Hilbert point is semistable. Indeed, Equation \ref{E:polarization} shows that the polarization
on $\overline{H}_{g,1}^{\, 3}/\hspace{-0.25pc}/ \operatorname{SL}(g)$ is a multiple of
\begin{equation}\label{E:slope-3}
\left(\frac{22}{3}+\frac{5}{g}\right)\lambda-\delta.
\end{equation}
On the other hand, the maximal possible slope for a family of generically smooth trigonal curves of genus $g$
 is $36(g+1)/(5g+1)$ by \cite{stankova}.
We note that $$36(g+1)/(5g+1)\leq \left(\frac{22}{3}+\frac{5}{g}\right)$$ whenever $(g-3)(2g-5)\geq 0$. Thus we expect that the $3^{rd}$ Hilbert
point of a genus $g\geq 4$ canonically embedded trigonal curve is stable.
\end{remark}

\bibliographystyle{alpha}

redpajama_set_name: RedPajamaArXiv