Examples of Fano manifolds with non-pseudoeffective tangent bundle

Andreas Höring; Jie Liu; Feng Shao

paper

Examples of Fano manifolds with non-pseudoeffective tangent bundle

arXiv:2003.09476

Abstract

Let $X$ be a Fano manifold. While the properties of the anticanonical divisor $- K_{X}$ and its multiples have been studied by many authors, the positivity of the tangent bundle $T_{X}$ is much more elusive. We give a complete characterisation of the pseudoeffectivity of $T_{X}$ for del Pezzo surfaces, hypersurfaces in the projective space and del Pezzo threefolds.

30 pages