  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 $i_F \leq r$.
