Smooth projective surfaces with pseudo-effective tangent bundles

Abstract

Let S be a non-uniruled (i.e., non-birationally ruled) smooth projective surface. We show that the tangent bundle TS is pseudo-effective if and only if the canonical divisor KS is nef and the second Chern class vanishes, i.e., c2(S) = 0. Moreover, we study the blow-up of a non-rational ruled surface with pseudo-effective tangent bundle. ©2024 The Mathematical Society of Japan.