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arXiv · 0903.4125

A Simple Characterization of Du Bois Singularities

Karl Schwede
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Abstract

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.

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Karl Schwede. 2009-03-24. A Simple Characterization of Du Bois Singularities. https://arxiv.org/abs/0903.4125

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