Algebraic Geometry Seminar
Kevin Tucker
UIC
Bertini Theorems for F-signature and Hilbert-Kunz Multiplicity
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.
Wednesday February 21, 2018 at 4:00 PM in SEO 427