Bigness of tangent bundles of blow-ups of ruled surfaces

Abstract

We determine when the bigness of the tangent bundle is preserved under point blow-ups of a ruled surface $S={\mathbb{P}}_C(\mathcal{E})$, giving a sharp bound on the number of blow-up points in terms of the first Segre invariant $s_1(\mathcal{E})$.

7 pages, 2 figures