Bigness of the tangent bundles of projective bundles over curves

TL;DR

This paper investigates the conditions under which the tangent bundle of a projective bundle over a curve is big, providing criteria based on the properties of the underlying vector bundle.

Contribution

It determines the bigness of the tangent bundle of projective bundles over curves, offering new insights into their geometric properties.

Findings

Criteria for the bigness of tangent bundles on projective bundles

Relationship between vector bundle properties and tangent bundle positivity

Conditions under which the tangent bundle is not big

Abstract

In this short article, we determine the bigness of the tangent bundle $T_X$ of the projective bundle $X=\mathbb{P}_C(E)$ associated to a vector bundle $E$ on a smooth projective curve $C$.