Algebraic Geometry Seminar
Karl Schwede
The Pennsylvania State University
Inversion of adjunction for rational and Du Bois pairs
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.
Tuesday November 26, 2013 at 12:00 PM in SEO 1227