Potentially Du Bois spaces
Journal of Singularities, Tome 8 (2014), pp. 117-134
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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 potentially Du Bois singularities coincide. In contrast, we give an example showing that in dimension at least three, a normal potentially Du Bois singularity x in X need not be Du Bois even if one assumes the canonical divisor K_X to be Q-Cartier.
@article{10_5427_jsing_2014_8i,
author = {Patrick Graf and S\'andor J. Kov\'acs},
title = {Potentially {Du} {Bois} spaces},
journal = {Journal of Singularities},
pages = {117--134},
publisher = {mathdoc},
volume = {8},
year = {2014},
doi = {10.5427/jsing.2014.8i},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2014.8i/}
}
Patrick Graf; Sándor J. Kovács. Potentially Du Bois spaces. Journal of Singularities, Tome 8 (2014), pp. 117-134. doi: 10.5427/jsing.2014.8i
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