# Du Bois singularity

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In algebraic geometry, **Du Bois singularities** are singularities of complex varieties studied by
Template:Harvtxt.

Template:Harvtxt 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.

## References

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