Back to Algebraic Geometry Seminar: Spring 2014
Algebraic Geometry Seminar
Date: Wednesday, Feb 12, 2014
Time: 3:30PM - 4:30PM
Location: LCB 215
(Wednesday) Time/Location: 2pm/LCB 222
Karl Schwede
Penn State University
Title |
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, for pairs, many recent results on Du Bois singularities. I will describe some of these ideas. This is joint work with Sandor Kovács. |
Algebraic Geometry