Karl Schwede

Log canonical and Du Bois singularities

Abstract: The following is joint work with S\'andor Kov\'acs and Karen Smith. In this talk I will describe a simple new Kempf-like characterization of Du Bois singularities in the normal Cohen-Macaulay case and explain how it can be used to show that Cohen-Macaulay (semi-)log canonical singularities are Du Bois, a conjecture of Koll\'ar. As a corollary, we obtain generalizations to Kodaira-type vanishing theorems.