English

On generic nefness of tangent sheaves

Algebraic Geometry 2021-08-03 v4

Abstract

We show that the tangent bundle of a projective manifold with nef anticanonical class is generically nef. That is, its restriction to a curve cut out by general sufficiently ample divisors is a nef vector bundle. This confirms a conjecture of Peternell. As a consequence, the second Chern class of such a manifold has non-negative intersections with ample divisors. We also investigate under which conditions these positivities are strict, and answer a question of Yau.

Keywords

Cite

@article{arxiv.1703.03175,
  title  = {On generic nefness of tangent sheaves},
  author = {Wenhao Ou},
  journal= {arXiv preprint arXiv:1703.03175},
  year   = {2021}
}