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Journal of the American Mathematical Society

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ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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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

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