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Varieties with ample cotangent bundle

Published online by Cambridge University Press:  04 December 2007

Olivier Debarre
Olivier Debarre
Affiliation:
Institut de Recherche Mathématique Avancée, Université Louis Pasteur, 7 rue René Descartes, F-67084 Strasbourg cedex, Francedebarre@math.u-strasbg.fr
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Abstract

The aim of this article is to provide methods for constructing smooth projective complex varieties with ample cotangent bundle. We prove that the intersection of at least n/2 sufficiently ample general hypersurfaces in a complex abelian variety of dimension n has ample cotangent bundle. We also discuss analogous questions for complete intersections in the projective space. Finally, we present an unpublished result of Bogomolov which states that a general linear section of small dimension of a product of sufficiently many smooth projective varieties with big cotangent bundle has ample cotangent bundle.

Keywords

ample cotangent bundle complete intersections 14K12 (primary) 14M10 14F10 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 6 , November 2005 , pp. 1445 - 1459
Copyright
Foundation Compositio Mathematica 2005

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