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

Part of: (Co)homology theory Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  11 December 2009

Daniel Greb ,
Stefan Kebekus  and
Sándor J. Kovács
Daniel Greb
Affiliation:
Albert-Ludwigs-Universität Freiburg, Mathematisches Institut, Eckerstrasse 1, 79104 Freiburg im Breisgau, Germany (email: [email protected])
Stefan Kebekus
Affiliation:
Albert-Ludwigs-Universität Freiburg, Mathematisches Institut, Eckerstrasse 1, 79104 Freiburg im Breisgau, Germany (email: [email protected])
Sándor J. Kovács
Affiliation:
University of Washington, Department of Mathematics, Box 354350, Seattle, WA 98195, USA (email: [email protected])
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Abstract

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Given a normal variety Z, a p-form σ defined on the smooth locus of Z and a resolution of singularities , we study the problem of extending the pull-back π*(σ) over the π-exceptional set . For log canonical pairs and for certain values of p, we show that an extension always exists, possibly with logarithmic poles along E. 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.

Keywords

differential formslog canonicalvanishing theorems

MSC classification

Secondary: 14J17: Singularities 14F17: Vanishing theorems
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 1 , January 2010 , pp. 193 - 219
Copyright
Copyright © Foundation Compositio Mathematica 2009

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