Du Bois singularity

In algebraic geometry, Du Bois singularities are singularities of complex varieties studied by . 
 gave the following characterisation of Du Bois singularities. Suppose that formula_1 is a reduced closed subscheme of a smooth scheme formula_2.
Take a log resolution formula_3 of formula_1 in formula_2 that is an isomorphism outside formula_1, and let formula_7 be the reduced preimage of formula_1 in formula_9. Then formula_1 has Du Bois singularities if and only if the induced map formula_11 is a quasi-isomorphism.