Compositio Mathematica

Rational, Log Canonical, Du Bois Singularities II: Kodaira Vanishing and Small Deformations

Sándor J. Kovács a1
a1 Department of Mathematics, University of Chicago, IL 60637, U.S.A. E-mail: or

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Kollár's conjecture, that log canonical singularities are Du Bois, is proved in the case of Cohen–Macaulay 3-folds. This in turn is used to derive Kodaira vanishing for this class of varieties. Finally it is proved that small deformations of Du Bois singularities are again Du Bois.

Key Words: singularities; rational; log canonical; Du Bois.