Varieties with ample cotangent bundle

Olivier Debarre
2005 Compositio Mathematica  
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 Finally, we present an unpublished result of Bogomolov which states that a general linear section of small dimension of a
more » ... ll dimension of a product of sufficiently many smooth projective varieties with big cotangent bundle has ample cotangent bundle.
doi:10.1112/s0010437x05001399 fatcat:q2p2tvi4tfbthoh2djfrebvqcu