Regular subdivisions and bounds on initial ideals

Abstract: We extend two known constructions that relate regular subdivisions to initial degenerations of projective toric varieties and Grassmannians. We associate a point configuration A with any homogeneous ideal I. We obtain upper and lower bounds on each initial ideal of I in terms of regular subdivisions of A. We also investigate when these bounds are exact, for example, the lower bound is exact for every initial ideal of the Plücker ideal I(2,n) with respect to points in the tropicalization. This talk is based on joint work with Dan Corey, Igor Makhlin, and Victoria Schleis.

algebraic geometrycombinatorics

Audience: researchers in the topic

Tropical Geometry in Frankfurt/Zoom TGiF/Z

Series comments: Description: An afternoon seminar series on tropical geometry, known as the TGiZ ("Tropical Geometry in Zoom") or the TGiF ("Tropical Geometry in Frankfurt") seminar.

Please send an email to one of the organizers at the latest one day before a session if you wish to receive the Zoom link and password.

Videos of some past talks are available on YouTube here, while some slides can be found here.