Projective manifolds whose tangent bundle contains a strictly nef subsheaf

Jie Liu; Wenhao Ou; Xiaokui Yang

Projective manifolds whose tangent bundle contains a strictly nef subsheaf

Algebraic Geometry 2020-04-21 v1 Complex Variables Differential Geometry

Authors: Jie Liu , Wenhao Ou , Xiaokui Yang

Abstract

Suppose that $X$ is a projective manifold whose tangent bundle $T_X$ contains a locally free strictly nef subsheaf. We prove that $X$ is isomorphic to a projective bundle over a hyperbolic manifold. Moreover, if the fundamental group $\pi_1(X)$ is virtually abelian, then $X$ is isomorphic to a projective space.

Keywords

nef and ample line bundles tangent bundle vector bundles

Cite

@article{arxiv.2004.08507,
  title  = {Projective manifolds whose tangent bundle contains a strictly nef subsheaf},
  author = {Jie Liu and Wenhao Ou and Xiaokui Yang},
  journal= {arXiv preprint arXiv:2004.08507},
  year   = {2020}
}

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