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Varieties With Ample Cotangent Bundle

O. Debarre
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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.

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O. Debarre. 2011-09-07. Varieties With Ample Cotangent Bundle. https://arxiv.org/abs/math/0306066

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