In algebraic geometry, Du Bois singularities are singularities of complex varieties studied by Du Bois.
Schwede gave the following characterisation of Du Bois singularities. Suppose that is a reduced closed subscheme of a smooth scheme .
Take a log resolution of in that is an isomorphism outside , and let be the reduced preimage of in . Then has Du Bois singularities if and only if the induced map is a quasi-isomorphism.