Geodesic
An optimal extension theorem for 1-forms and the Lipman-Zariski conjecture
Documenta mathematica, Tome 19 (2014), pp. 815-830.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\wt X \to X$ 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.
Classification : 14B05, 32S05
Keywords: singularities of the minimal model program, differential forms, lipman-Zariski conjecture 
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     author = {Graf, Patrick and Kov\'acs, S\'andor J.},
     title = {An optimal extension theorem for 1-forms and the {Lipman-Zariski} conjecture},
     journal = {Documenta mathematica},
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     publisher = {mathdoc},
     volume = {19},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a18/}
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Graf, Patrick; Kovács, Sándor J. An optimal extension theorem for 1-forms and the Lipman-Zariski conjecture. Documenta mathematica, Tome 19 (2014), pp. 815-830. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a18/