Karl Schwede : F-signature and relations to algebraic geometry

Posted by , part of the Algebraic Geometry Seminar.

At

March 7, 2012, 4 p.m.

In

SEO 427

Abstract

The F-signature of a local ring R of characteristic p > 0 is a real number which reflects the severity of the singularities of R. It was introduced explicitly by C. Huneke and G. Leuschke building upon work of K. Smith and M. Van den Bergh. In this talk, I will explain some of its history, and its recent generalization to the context of pairs. I will also explain connections to the minimal log discrepancy and how the F-signature might be useful for studying geometric questions in the future. Most of what is discussed is joint work with Manuel Blickle and Kevin Tucker.