Geodesic
An optimal extension theorem for 1-forms and the Lipman–Zariski conjecture
Documenta mathematica, Tome 19 (2014), pp. 815-830
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Let X be a normal variety. Assume that for some reduced divisor D⊂X, logarithmic 1-forms defined on the snc locus of (X,D) extend to a log resolution X→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,∅) which acquires a logarithmic pole along an exceptional divisor of discrepancy zero, thereby improving on a similar example of Greb, Kebekus, Kovács and Peternell.
DOI : 10.4171/dm/465
Classification : 14B05, 32S05
Mots-clés : differential forms, singularities of the minimal model program, lipman-Zariski conjecture 
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     author = {Patrick Graf and S\'andor J. Kov\'acs},
     title = {An optimal extension theorem for 1-forms and the {Lipman{\textendash}Zariski} conjecture},
     journal = {Documenta mathematica},
     pages = {815--830},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/465},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/465/}
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Patrick Graf; Sándor J. Kovács. An optimal extension theorem for 1-forms and the Lipman–Zariski conjecture. Documenta mathematica, Tome 19 (2014), pp. 815-830. doi: 10.4171/dm/465

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