Log canonical singularities are Du Bois

Kollár, János¹ ; Kovács, Sándor²

¹ Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000
² Department of Mathematics, University of Washington, Seattle, Washington 98195-4350

Journal of the American Mathematical Society, Tome 23 (2010) no. 3, pp. 791-813

Résumé

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.

Détail

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

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