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arXiv · 1307.3449

Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations

Andreas Höring
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Abstract

Let X be a normal projective variety, and let A be an ample Cartier divisor on X. We prove that the twisted cotangent sheaf $\Omega_X \otimes A$ is generically nef with respect to the polarisation A unless X is a projective space. As an application we prove a Kobayashi-Ochiai theorem for foliations: if $F \subsetneq T_X$ is a foliation of rank r such that $det F \equiv i_F A$, then we have $i_F \leq r$.

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Andreas Höring. 2013-07-12. Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations. https://arxiv.org/abs/1307.3449

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