## Log canonical singularities are Du Bois

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- by János Kollár and Sándor J Kovács
- J. Amer. Math. Soc.
**23**(2010), 791-813 - DOI: https://doi.org/10.1090/S0894-0347-10-00663-6
- Published electronically: February 22, 2010
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Previous version: Original version posted February 12, 2010

Corrected version: Current version corrects publisher's introduction of inconsistent rendering of script O.

## Abstract:

A recurring difficulty in the Minimal Model Program is that while log terminal singularities are quite well behaved (for instance, they are rational), log canonical singularities are much more complicated; they need not even be Cohen-Macaulay. The aim of this paper is to prove that log canonical singularities are Du Bois. The concept of Du Bois singularities, introduced by Steenbrink, is a weakening of rationality. We also prove flatness of the cohomology sheaves of the relative dualizing complex of a projective family with Du Bois fibers. This implies that each connected component of the moduli space of stable log varieties parametrizes either only Cohen-Macaulay or only non-Cohen-Macaulay objects.## References

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## Bibliographic Information

**János Kollár**- Affiliation: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000
- MR Author ID: 104280
- Email: kollar@math.princeton.edu
**Sándor J Kovács**- Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
- MR Author ID: 289685
- Email: skovacs@uw.edu
- Received by editor(s): April 27, 2009
- Received by editor(s) in revised form: November 30, 2009
- Published electronically: February 22, 2010
- Additional Notes: The first author was supported in part by NSF Grant DMS-0758275.

The second author was supported in part by NSF Grants DMS-0554697 and DMS-0856185 and the Craig McKibben and Sarah Merner Endowed Professorship in Mathematics - © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc.
**23**(2010), 791-813 - MSC (2010): Primary 14J17, 14B07, 14E30, 14D99
- DOI: https://doi.org/10.1090/S0894-0347-10-00663-6
- MathSciNet review: 2629988