Log canonical singularities are Du Bois

By J. Kollár, S'andor J. Kov'acs. 2009

237 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a6c1ff403e5bcf66fe421eec45d43d6a9470f9f7

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Citations in the corpus

Remarks on degenerations of hyper-K\"ahler manifolds (2017, background): “Namely, as explained in Section 3, as a consequence of [38] and [73], as long as X0 is semi log canonical (e.”
The global moduli theory of symplectic varieties (2018, background): “tion); (2)the pair (X ;X) is Q-factorial and dlt (see for example [BCHM10, 3.10.9]); (3) K X is f-numerically trivial.7 By adjunction (see for example [Kol13, Theorem 4.9]), X is slc and thus du Bois [KK10], so by Lemma7.4we have that Xis symplectic. Take a Q-factorial terminalization Xe! Xand pull ”
On a generalized canonical bundle formula and generalized adjunction (2018, background): “We refer to [30] for a more detailed discussion of the topic.”
Hodge theory meets the minimal model program: a survey of log canonical and Du Bois singularities (2009, methodology): “Here we give a different proof than in [KK09].”
Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, background): “e varieties with given numerical invariants. These assertions have been proven in dimensions ≤ 2 [Ale94], but remain open in higher dimensions. Remark 6.1.6. The discussion following Corollary 1.3 of [KK09] implies that the stable limit of a one-parameter family of Cohen-Macaulay stable varieties (r”