Kevin Tucker : Bertini Theorems for F-signature and Hilbert-Kunz Multiplicity

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

At

Feb. 21, 2018, 4 p.m.

In

SEO 427

Abstract

In characteristic zero, it is well known that multiplier ideals and log terminal singularities satisfy Bertini-type theorems for hyperplane sections. The analogous situation in characteristic p > 0 is more complicated. While F-regular singularities satisfy Bertini, the test ideal does not. In this talk, I will describe joint work with Karl Schwede and Javier Carvajal-Rojas showing that the F-signature -- a numerical invariant of singularities that detects F-regularity -- satisfies the relevant Bertini statements for hyperplane sections. In particular, one can view this as a generalization of the corresponding results for F-regularity.