The canonical sheaf of Du Bois singularities |
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Authors: | Sándor J Kovács Karl Schwede Karen E Smith |
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Institution: | a University of Washington, Department of Mathematics, Seattle, WA 98195, USA b Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA |
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Abstract: | We prove that a Cohen-Macaulay normal variety X has Du Bois singularities if and only if π∗ωX′(G)?ωX for a log resolution π:X′→X, where G is the reduced exceptional divisor of π. Many basic theorems about Du Bois singularities become transparent using this characterization (including the fact that Cohen-Macaulay log canonical singularities are Du Bois). We also give a straightforward and self-contained proof that (generalizations of) semi-log-canonical singularities are Du Bois, in the Cohen-Macaulay case. It also follows that the Kodaira vanishing theorem holds for semi-log-canonical varieties and that Cohen-Macaulay semi-log-canonical singularities are cohomologically insignificant in the sense of Dolgachev. |
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