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→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 Rπ*OE is a quasi-isomorphism.
References
* Du Bois, Philippe (1981), "Complexe de de Rham filtré d'une variété singulière", Bulletin de la Société Mathématique de France 109 (1): 41–81, MR613848, ISSN 0037-9484, http://www.numdam.org/item?id=BSMF_1981__109__41_0
* Schwede, Karl (2007), "A simple characterization of Du Bois singularities", Compositio Mathematica 143 (4): 813–828, doi:10.1112/S0010437X07003004, MR2339829, ISSN 0010-437X
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