Nathan Ilten-Gee (SFU)

Tuesday, May 9, 2023 - 1:45pm

PDL C-38

For the pretalk:

Title: Equivariant vector bundles on toric varieties

Abstract: I will recall some basic notions of toric geometry, and discuss Klyachko's description of equivariant vector bundles on toric varieties in terms of collections of filtrations.

For the talk:

Title: Local euler characteristic for symmetric differentials on A_n singularities

Abstract: Local euler characteristic, introduced by Wahl, is a measure of how a reflexive sheaf on a surface singularity changes when passing to a resolution of the singularity. Recently it has been used by Bruin, Thomas, and Várilly-Alvarado in the study of algebraic quasi-hyperbolicity for singular surfaces. In this talk, I will give an explicit formula for the local Euler characteristic of the mth symmetric power of the sheaf of differentials on an A_n singularity. In particular, I will show that the local Euler characteristic is a quasipolynomial in m of period n+1. The proof makes use of tools from toric geometry and Ehrhart theory and involves some fun combinatorics. This is joint work in progress with Nils Bruin and Zhe Xu.