Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations

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 $F⊊T_X$ is a foliation of rank r such that $detF\equiv i_{F}A$, then we have $i_F\le r$.

arXiv comment13 pages, changed metadata