Potentially Du Bois spaces

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