Smooth projective surfaces with pseudo-effective tangent bundles

Jia Jia; Yongnam Lee; Guolei Zhong

paper

Smooth projective surfaces with pseudo-effective tangent bundles

arXiv:2302.10077

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.

arXiv commentRemark 1.7 and references are updated