UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

September 11, 2012

939 Evans Hall

3:45PM: Torus quotients of binomial D-modules.

Christine Berkesch

Binomial D-modules are given by a binomial ideal and homogeneity operators. I will explain how combinatorial tools from toric geometry have been successful at analyzing many aspects of binomial D-modules, which carry a torus action. We will then consider how to take a quotient by this action, with the goal of gaining a new understanding of the classical hypergeometric systems studied by, among others, Gauss, Appell, and Lauricella. This is joint work with Laura Felicia Matusevich and Uli Walther.

5:00PM: A characterization of toric varieties in characteristic p

Piotr Achinger

A theorem of J. F. Thomsen states that Frobenius push-forwards of line bundles on smooth toric varieties are direct sums of line bundles. Using characterization of toric varieties in terms of their Cox rings, we show that this property in fact characterizes smooth projective toric varieties.

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