The canonical sheaf of Du Bois singularities

By S'andor J. Kov'acs, Karl Schwede, Karen E. Smith. 2008

74 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/227302ce5c4a88abb16573d25d801886e3865420

How researchers see this paper

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In Algebra and Number Theory

1. O. Fujino
2. S'andor J. Kov'acs
3. Karl Schwede
4. Henri Guenancia
5. Robert J. Berman
6. Christopher D. Hacon
7. Kevin Tucker
8. Manuel Blickle

In Computational Theory and Mathematics

1. O. Fujino
2. Karl Schwede
3. Henri Guenancia
4. S'andor J. Kov'acs
5. Robert J. Berman
6. C. Birkar
7. Christopher D. Hacon
8. Hiromu Tanaka

In Geometry and Topology

1. O. Fujino
2. S'andor J. Kov'acs
3. Karl Schwede
4. Henri Guenancia
5. Robert J. Berman
6. Christopher D. Hacon
7. Chi Li
8. Chenyang Xu

Citations in the corpus

• Fundamental theorems for semi log canonical pairs (2012, methodology): “ova´cs–Schwede– Smith. For the details, see [KSS, Corollary 6.6]. In general, X is not Cohen–Macaulay. Therefore, the dual form of the Kodaira vanishing theorem does not always hold. The arguments in [KSS] are based on the theory of Du Bois singularities (see, for example, [KSS], [KK], and [Ko5, Cha”
• Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs (2013, result): “We refer to [ Tra70, GT80, KSS10 ]) for the previous assertions.”
• Hodge theory meets the minimal model program: a survey of log canonical and Du Bois singularities (2009, background): “Related results can also be obtained in the non-normal Cohen-Macaulay case, see [KSS08] for details.”