LOG CANONICAL SINGULARITIES ARE DU BOIS

摘要

A recurring difficulty in the Minimal Model Program (MMP) 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, as conjectured in [Ko192, 1.13], log canonical singularities are Du Bois. The concept of Du Bois singularities, abbreviated as DB, was introduced by Steenbrink in [Ste83] as a weakening of rationality. It is not clear how to define Du Bois singularities in positive characteristic, so we work over a field of characteristic 0 throughout the paper. The precise definition is rather involved, see (1.10), but our main applications rely only on the following consequence.