# Potentially Du Bois spaces

@article{Graf2014PotentiallyDB, title={Potentially Du Bois spaces}, author={Patrick Graf and S'andor J. Kov'acs}, journal={arXiv: Algebraic Geometry}, year={2014} }

We investigate properties of potentially Du Bois singularities, that is, those that occur on the underlying space of a Du Bois pair. We show that a normal variety $X$ with potentially Du Bois singularities and Cartier canonical divisor $K_X$ is necessarily log canonical, and hence Du Bois. As an immediate corollary, we obtain the Lipman-Zariski conjecture for varieties with potentially Du Bois singularities.
We also show that for a normal surface singularity, the notions of Du Bois and… Expand

#### 10 Citations

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We prove that the cohomology sheaves of the relative dualizing complex of a flat family of varieties with semi-log-canonical or Du Bois singularities are flat and commute with base change. This is a… Expand

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