Extension theorems for differential forms and Bogomolov-Sommese vanishing on log canonical varieties

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Greb, Daniel
Kebekus, Stefan
Kovács, Sándor J.
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Abstract
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Given a p-form defined on the smooth locus of a normal variety, and a resolution of singularities, we study the problem of extending the pull-back of the p-form over the exceptional set of the desingularization. For log canonical pairs and for certain values of p, we show that an extension always exists, possibly with logarithmic poles along the exceptional set. As a corollary, it is shown that sheaves of reflexive differentials enjoy good pull-back properties. A natural generalization of the well-known Bogomolov-Sommese vanishing theorem to log canonical threefold pairs follows.
Comment: final version with improved exposition and several minor clarifications and corrections
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Mathematics - Algebraic Geometry, 14J17, 14F17
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