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arXiv · 0902.0648

Log canonical singularities are Du Bois

János Kollár·Sándor J Kovács
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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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János Kollár, Sándor J Kovács. 2009-02-04. Log canonical singularities are Du Bois. https://doi.org/10.1090/s0894-0347-10-00663-6

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