Journal of Singularities
volume 8 (2014), 117-134
Received: 18 February 2014. Received in revised form: 14 October 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 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.
Singularities of the minimal model program, Du Bois pairs, differential forms, Lipman-Zariski conjecture
Mathematical Subject Classification:
|Patrick Graf||Sándor Kovács|
|Lehrstuhl für Mathematik I||Department of Mathematics, Box 354350|
|Universität Bayreuth||University of Washington|
|95440 Bayreuth, Germany||Seattle, WA 98195-4350, USA|
|email: firstname.lastname@example.org||email: email@example.com|