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 $$X$$ is a reduced closed subscheme of a smooth scheme $$Y$$.

Take a log resolution $$\pi: Z \to Y$$ 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 $$\mathcal{O}_X \to R\pi_{*}\mathcal{O}_E$$ is a quasi-isomorphism.