Projective manifolds whose tangent bundle contains a strictly nef subsheaf

Abstract: After a theorem of Andreatta and Wisniewski, if the tangent bundle of a projective manifold $X$ contains an ample subsheaf, then $X$ is isomorphic to the projective space. We show that, if the tangent bundle contains a strictly nef subsheaf, then X is a projective bundle over a hyperbolic manifold. Moreover, if the fundamental group of $X$ is virtually abelian, then $X$ is isomorphic to a projective space. This is joint with Jie Liu and Xiaokui Yang.

Mathematics

Audience: researchers in the topic

ICCM 2020