Kevin Tucker : Fundamental Groups of F-regular Singularities via F-Signature

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

At

Aug. 31, 2016, 4 p.m.

In

SEO 427

Abstract

The F-signature is a numerical invariant of singularities which measures the asymptotic number of splittings of iterates of Frobenius. The positivity of the F-signature characterizes F-regular singularities, which are closely related to KLT singularities in characteristic zero. After giving an overview, I will discuss new transformation rules for F-signature under finite maps. These transformation rules allow us to show finiteness of the etale local fundamental group for F-regular singularities, analogous to results of Xu and Greb-Kebekus-Peternell for KLT singularities in characteristic zero. This is joint work with Javier Cravajal-Rojas and Karl Schwede.