Varieties With Ample Cotangent Bundle
Abstract
We study smooth projective complex varieties with ample cotangent bundle. Our main result is that in an abelian variety of dimension n, a complete intersection of at least n/2 general hypersurfaces of sufficiently high degrees has ample cotangent bundle. We discuss the conjecture that the analogous statement should hold in the projective space. Finally, we present a construction due to Bogomolov of varieties with ample cotangent bundle as linear sections of a product of varieties with big cotangent bundle.
Cite
@article{arxiv.math/0306066,
title = {Varieties With Ample Cotangent Bundle},
author = {O. Debarre},
journal= {arXiv preprint arXiv:math/0306066},
year = {2011}
}
Comments
We correct several inaccuracies. In particular, the main lemma (whose statement was incorrect) is replaced with a result of O. Benoist (arXiv:0911.1118v1). A particular case of the conjecture in the projective space was recently proved by D. Brotbek (arXiv:1101.3394v1)