Log canonical singularities are Du Bois

Kollár, János; Kovács, Sándor

doi:10.1090/S0894-0347-10-00663-6

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.

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