Compositio Mathematica

A simple characterization of Du Bois singularities

Karl Schwede a1
a1 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA [email protected]

Article author query
schwede k   [Google Scholar] 


We prove the following theorem characterizing Du Bois singularities. Suppose that $Y$ is smooth and that $X$ is a reduced closed subscheme. Let $\pi : \tilde{Y} \rightarrow Y$ be a log resolution of $X$ in $Y$ that is an isomorphism outside of $X$. If $E$ is the reduced pre-image of $X$ in $\tilde{Y}$, then $X$ has Du Bois singularities if and only if the natural map $\mathcal{O}_X \rightarrow R \pi_* \mathcal{O}_E$ is a quasi-isomorphism. We also deduce Kollár's conjecture that log canonical singularities are Du Bois in the special case of a local complete intersection and prove other results related to adjunction.

(Published Online July 17 2007)
(Received October 3 2006)
(Accepted March 3 2007)

Key Words: singularities; rational; log canonical; Du Bois; adjunction; multiplier ideals.

Maths Classification


Dedicated to Jozef Steenbrink on the occasion of his 60th birthday