Log canonical singularities are Du Bois

Details Log canonical singularities are Du Bois Log canonical singularities are Du Bois

2009-02-04

arxiv.org/abs/0902.0648v4

Mathematics

Algebraic Geometry

An error discovered in the statement and proof of Theorem 1.7 is corrected. Note that this change does not effect the rest of

Scientific paper

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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