Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

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

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

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Log canonical singularities are Du Bois
HTML articles powered by AMS MathViewer

by János Kollár and Sándor J Kovács
J. Amer. Math. Soc. 23 (2010), 791-813
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.


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.
Similar Articles
Bibliographic Information
  • János Kollár
  • Affiliation: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000
  • MR Author ID: 104280
  • Email:
  • Sándor J Kovács
  • Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
  • MR Author ID: 289685
  • Email:
  • 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:
  • MathSciNet review: 2629988