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High Quality Content by WIKIPEDIA articles! 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 :Z Y 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 from OX to R OE is a quasi-isomorphism.