Feng Shao, The Bigness of Tangent Bundles of Projective Manifolds

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. In this talk, we give a complete characterization of the pseudoeffectivity and the bigness of T_X for del Pezzo surfaces, hypersurfaces in the projective space and del Pezzo threefolds.