Geometric stability of the cotangent bundle and the universal cover of a projective manifold

Campana, Frederic; Peternell, Thomas; Toma, Matei

Geometric stability of the cotangent bundle and the universal cover of a projective manifold

Authors

Campana, Frederic

Peternell, Thomas

Toma, Matei

Description

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 non-uniruled manifold: this bundle is always pseudo-effective. 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 Q-divisor, then the Kodaira dimension is non-negative.
Latex, 29 pages, appendix by Matei Toma added; rest unchanged