Student Arithmetic Geometry Seminar: Uniqueness Properties for Spherical Varieties

Seminar | March 1 | 4:10-5 p.m. | 891 Evans Hall

 Alexander Sherman, UCB

 Department of Mathematics

Toric varieties are varieties with an action of a torus having an open orbit. Spherical varieties are natural generalizations, having an action of reductive group with an open Borel orbit. Like with toric varieties, there are natural combinatorial invariants that one can define from a spherical variety, such as the irreducible summands which appear in the ring of regular functions. Losev proved that, for the case of (smooth) affine spherical varieties and the case of homogeneous spherical varieties, these combinatorial invariants uniquely determine the variety with the G-action.

We will define spherical varieties and the combinatorial invariants involved, giving examples. Then we'll state the theorems due to Losev. Time permitting, we'll also discuss some ideas of the proof, along with other results related to these theorems.