A Simple Characterization of Du Bois Singularities
Abstract
Description
We prove the following theorem characterizing Du Bois singularities. Suppose that $Y$ is smooth and that $X$ is a reduced closed subscheme. Let $π: \tld Y \to Y$ 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 $\tld Y$, then $X$ has Du Bois singularities if and only if the natural map $Ø_X \to R π_* Ø_E$ 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.
17 pages; the final version appeared in Compositio Mathematica in 2007, http://www.journals.cambridge.org/action/displayAbstract;jsessionid=87324D164BF30982691FD683E4B588BC.tomcat1?fromPage=online&aid=1207968
17 pages; the final version appeared in Compositio Mathematica in 2007, http://www.journals.cambridge.org/action/displayAbstract;jsessionid=87324D164BF30982691FD683E4B588BC.tomcat1?fromPage=online&aid=1207968