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

Frederic Campana·Thomas Peternell·Matei Toma
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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 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.

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Frederic Campana, Thomas Peternell, Matei Toma. 2007-11-12. Geometric stability of the cotangent bundle and the universal cover of a projective manifold. https://arxiv.org/abs/math/0405093

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