'modDate': 'D:20210622012710Z', 'trapped': '', 'encryption': None}, lookup_index=0)Fetching remote PDFs using Unstructured‚ÄãThis covers how to load online PDFs into a document format that we can use downstream. This can be used for various online PDF sites such as https://open.umn.edu/opentextbooks/textbooks/ and https://arxiv.org/archive/Note: all other PDF loaders can also be used to fetch remote PDFs, but OnlinePDFLoader is a legacy function, and works specifically with UnstructuredPDFLoader.from langchain.document_loaders import OnlinePDFLoaderloader = OnlinePDFLoader("https://arxiv.org/pdf/2302.03803.pdf")data = loader.load()print(data)    [Document(page_content='A WEAK ( k, k ) -LEFSCHETZ THEOREM FOR PROJECTIVE TORIC ORBIFOLDS\n\nWilliam D. Montoya\n\nInstituto de Matem¬¥atica, Estat¬¥ƒ±stica e Computa¬∏cÀúao Cient¬¥ƒ±Ô¨Åca,\n\nIn [3] we proved that, under suitable conditions, on a very general codimension s quasi- smooth intersection subvariety X in a projective toric orbifold P d Œ£ with d + s = 2 ( k + 1 ) the Hodge conjecture holds, that is, every ( p, p ) -cohomology class, under the Poincar¬¥e duality is a rational linear combination of fundamental classes of algebraic subvarieties of X . The proof of the above-mentioned result relies, for p ‚â† d + 1 ‚àí s , on a Lefschetz\n\nKeywords: (1,1)- Lefschetz theorem, Hodge conjecture, toric varieties, complete intersection Email: wmontoya@ime.unicamp.br\n\ntheorem ([7]) and the Hard Lefschetz theorem for projective orbifolds ([11]). When p = d + 1 ‚àí s the proof relies on the Cayley trick, a trick which associates to X a quasi-smooth hypersurface Y in a projective vector bundle, and the Cayley Proposition (4.3) which gives an isomorphism of some primitive cohomologies (4.2) of X and Y . The Cayley trick, following the philosophy of Mavlyutov in [7], reduces results known for quasi-smooth hypersurfaces to quasi-smooth intersection subvarieties. The idea in this paper goes the other way around, we translate
Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems.
Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems. ->: 'modDate': 'D:20210622012710Z', 'trapped': '', 'encryption': None}, lookup_index=0)Fetching remote PDFs using Unstructured‚ÄãThis covers how to load online PDFs into a document format that we can use downstream. This can be used for various online PDF sites such as https://open.umn.edu/opentextbooks/textbooks/ and https://arxiv.org/archive/Note: all other PDF loaders can also be used to fetch remote PDFs, but OnlinePDFLoader is a legacy function, and works specifically with UnstructuredPDFLoader.from langchain.document_loaders import OnlinePDFLoaderloader = OnlinePDFLoader("https://arxiv.org/pdf/2302.03803.pdf")data = loader.load()print(data)    [Document(page_content='A WEAK ( k, k ) -LEFSCHETZ THEOREM FOR PROJECTIVE TORIC ORBIFOLDS\n\nWilliam D. Montoya\n\nInstituto de Matem¬¥atica, Estat¬¥ƒ±stica e Computa¬∏cÀúao Cient¬¥ƒ±Ô¨Åca,\n\nIn [3] we proved that, under suitable conditions, on a very general codimension s quasi- smooth intersection subvariety X in a projective toric orbifold P d Œ£ with d + s = 2 ( k + 1 ) the Hodge conjecture holds, that is, every ( p, p ) -cohomology class, under the Poincar¬¥e duality is a rational linear combination of fundamental classes of algebraic subvarieties of X . The proof of the above-mentioned result relies, for p ‚â† d + 1 ‚àí s , on a Lefschetz\n\nKeywords: (1,1)- Lefschetz theorem, Hodge conjecture, toric varieties, complete intersection Email: wmontoya@ime.unicamp.br\n\ntheorem ([7]) and the Hard Lefschetz theorem for projective orbifolds ([11]). When p = d + 1 ‚àí s the proof relies on the Cayley trick, a trick which associates to X a quasi-smooth hypersurface Y in a projective vector bundle, and the Cayley Proposition (4.3) which gives an isomorphism of some primitive cohomologies (4.2) of X and Y . The Cayley trick, following the philosophy of Mavlyutov in [7], reduces results known for quasi-smooth hypersurfaces to quasi-smooth intersection subvarieties. The idea in this paper goes the other way around, we translate