Compositio Mathematica

Varieties with ample cotangent bundle

Olivier Debarre a1
a1 Institut de Recherche Mathématique Avancée, Université Louis Pasteur, 7 rue René Descartes, F-67084 Strasbourg cedex, France

Article author query
debarre o   [Google Scholar] 


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 Finally, we present an unpublished result of Bogomolov which states that a general linear section of small dimension of a product of sufficiently many smooth projective varieties with big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.

(Received May 18 2004)
(Accepted October 22 2004)

Key Words: ample cotangent bundle; complete intersections.

Maths Classification

14K12 (primary); 14M10; 14F10 (secondary).