Karl Schwede : Inversion of adjunction for rational and Du Bois pairs

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

At

Nov. 26, 2013, noon

In

SEO 1227

Abstract

We prove a new inversion of adjunction statement for rational and Du Bois singularities. Roughly speaking, this says that if we have a family over a smooth base with Du Bois special fiber and rational generic fiber, then the total space also has rational singularities. Furthermore, we even generalize this result to the context of rational and Du Bois pairs as defined by Kollár and Kovács. Imprecisely, a pair $(X, D)$ is Du Bois if the failure of $X$ to be Du Bois is equal to the failure of $D$ to be Du Bois. In order to accomplish our inversion of adjunction result we need to prove many recent results on Du Bois singularities for pairs, and I will describe some of these ideas. This is joint work with Sandor Kovács.