Abstract
Let X be a normal variety. Assume that for some reduced divisor D \subset X , logarithmic 1-forms defined on the snc locus of (X, D) extend to a log resolution \widetilde X \to X as logarithmic differential forms. We prove that then the Lipman–Zariski conjecture holds for X . This result applies in particular if X has log canonical singularities. Furthermore, we give an example of a 2-form defined on the smooth locus of a three-dimensional log canonical pair (X, \emptyset) which acquires a logarithmic pole along an exceptional divisor of discrepancy zero, thereby improving on a similar example of Greb, Kebekus, Kovács and Peternell.
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