Abstract
Let (X,D) be a projective log canonical pair. We show that for any natural number p, the sheaf
In fact, we prove a more general version of this result which also deals with the orbifoldes géométriques introduced by Campana. The main ingredients to the proof are the Extension Theorem of Greb–Kebekus–Kovács–Peternell, a new version of the Negativity Lemma, the minimal model program, and a residue map for symmetric differentials on dlt pairs.
We also give an example showing that the statement cannot be generalized to spaces with Du Bois singularities. As an application, we give a Kodaira–Akizuki–Nakano-type vanishing result for log canonical pairs which holds for reflexive as well as for Kähler differentials.
Funding source: DFG
Award Identifier / Grant number: Forschergruppe 790 “Classification of Algebraic Surfaces and Compact Complex Manifolds”
The results of this paper are part of the author's Ph.D. thesis. He would like to thank his supervisor, Stefan Kebekus, for fruitful advice and support. He would also like to thank the members of Kebekus' research group, especially Daniel Greb, Clemens Jörder, and Alex Küronya, as well as the research group's past guests, especially Kiwamu Watanabe, for interesting discussions. The author is particularly grateful to Stefan Kebekus, Alex Küronya, and the anonymous referee for valuable suggestions concerning the exposition of this paper.
© 2015 by De Gruyter
