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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

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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 Finally, we present an unpublished result of Bogomolov which states that a general linear section of small dimension of a product of sufficiently many smooth projective varieties with big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 bundlecomplete intersections14K12 (primary)14M1014F10 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 6 , November 2005 , pp. 1445 - 1459
Copyright
Foundation Compositio Mathematica 2005