Varieties with ample cotangent bundle
By O. Debarre. Compositio Mathematica, 2003
64 citations recorded by the source corpus.
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 Finally, we present an unpublished result of Bogomolov which states that a general linear section of small dimension of a product of sufficiently many smooth projective varieties with big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.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/901bacdeb6d2b229fd0b579f8d2fa5c0a72fa07c
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the hyperbolicity of general hypersurfaces (2016, background): “Considering jets of order one, recall that a conjecture of Debarre [11] predicts that a general complete intersection in Pn of high multidegree and of codimension larger than its dimension, has ample cotangent bundle.”