Du Bois singularity

In algebraic geometry, Du Bois singularities are singularities of complex varieties studied by Du Bois (1981).

Schwede (2007) gave the following characterisation of Du Bois singularities. Suppose that X is a reduced closed subscheme of a smooth scheme Y .

Take a log resolution π : Z → X of X in Y that is an isomorphism outside X , and let E be the reduced preimage of X in Z . Then X has Du Bois singularities if and only if the induced map O X → R π ∗ O E is a quasi-isomorphism.