Du Bois singularity

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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 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.