Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-04T19:12:48.589Z Has data issue: false hasContentIssue false

A simple characterization of Du Bois singularities

Published online by Cambridge University Press:  17 July 2007

Karl Schwede
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2007