Du Bois singularities and birational geometry
Karl Schwede, University of Washington

Abstract: Du Bois singularities were defined initially in Hodge theoretic contexts by Steenbrink based on a condition studied by Du Bois. However, they have long been known to be related to singularities of the minimal model program (rational singularities are Du Bois and it is conjectured that log canonical singularities are Du Bois). Unfortunately, the methods used to define Du Bois singularities are simplicial, and quite complicated in general. The main purpose of this talk will be to demonstrate that Du Bois singularities really ought to be defined beside log terminal, log canonical and rational singularities and I will discuss a new method to define them using only a single log resolution. I will use these techniques to establish interesting applications to rational singularities, a sort of inversion of adjunction, and additional progress towards the LC => Du Bois conjecture.