  An ideal $I$ is said to be "well-poised" if all of the initial ideals
obtained from points in the tropical variety $Trop(I)$ are prime. This
condition was first defined by Nathan Ilten and the third author. We classify
all well-poised hypersurfaces over an algebraically closed field. We also study
the tropical varieties and associated Newton-Okounkov bodies of these
hypersurfaces.

Algebraic Geometry