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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Log canonical singularities are Du Bois


Authors: János Kollár and Sándor J Kovács
Journal: J. Amer. Math. Soc. 23 (2010), 791-813
MSC (2010): Primary 14J17, 14B07, 14E30, 14D99
Published electronically: February 22, 2010
Previous version: Original version posted February 12, 2010
Corrected version: Current version corrects publisher's introduction of inconsistent rendering of script O.
MathSciNet review: 2629988
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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.


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Additional Information

János Kollár
Affiliation: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000
Email: kollar@math.princeton.edu

Sándor J Kovács
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
Email: skovacs@uw.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-10-00663-6
PII: S 0894-0347(10)00663-6
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.