Smooth projective surfaces with pseudo-effective tangent bundles

Jia Jia; Yongnam Lee; Guolei Zhong

Smooth projective surfaces with pseudo-effective tangent bundles

Algebraic Geometry 2023-05-02 v3

Authors: Jia Jia , Yongnam Lee , Guolei Zhong

Abstract

Let $S$ be a non-uniruled (i.e., non-birationally ruled) smooth projective surface. We show that the tangent bundle $T_S$ is pseudo-effective if and only if the canonical divisor $K_S$ is nef and the second Chern class vanishes, i.e., $c_2(S)=0$ . Moreover, we study the blow-up of a non-rational ruled surface with pseudo-effective tangent bundle.

Keywords

nef and ample line bundles vector bundles del pezzo surfaces

Cite

@article{arxiv.2302.10077,
  title  = {Smooth projective surfaces with pseudo-effective tangent bundles},
  author = {Jia Jia and Yongnam Lee and Guolei Zhong},
  journal= {arXiv preprint arXiv:2302.10077},
  year   = {2023}
}

Comments

Remark 1.7 and references are updated

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