Geometric stability of the cotangent bundle and the universal cover of a projective manifold
Abstract
Consider a projective manifold X and suppose that some wedge power of the cotangent bundle contains a subsheaf whose determinant bundle has maximal Kodaira dimension. Then we prove that X is of general type. More generally we compute the Kodaira dimension if the determinant bundle has sufficiently large Kodaira dimension. This is based on the study of the determinant bundle of a quotient of the cotangent bundle of a nonuniruled manifold: this bundle is always pseudoeffective. We apply this to study the universal cover of a projective manifold. Finally we prove the following: if the canonical bundle is numerically equivalent to an effective Qdivisor, then the Kodaira dimension is nonnegative.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2004
 arXiv:
 arXiv:math/0405093
 Bibcode:
 2004math......5093C
 Keywords:

 Mathematics  Algebraic Geometry;
 14E20;
 14E30
 EPrint:
 Latex, 29 pages, appendix by Matei Toma added