Varieties With Ample Cotangent Bundle

Details Varieties With Ample Cotangent Bundle Varieties With Ample Cotangent Bundle

2003-06-03

arxiv.org/abs/math/0306066v5

Mathematics

Algebraic Geometry

We correct several inaccuracies. In particular, the main lemma (whose statement was incorrect) is replaced with a result of O.

Scientific paper

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.

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