About the stability of the tangent bundle of P^n restricted to a surface

TL;DR

This paper investigates the stability of the tangent bundle of projective space restricted to various surfaces, providing conditions under which it remains -stable for different types of surfaces.

Contribution

It establishes new stability results for the tangent bundle restricted to surfaces like K3 and abelian surfaces under specific conditions.

Findings

-stability holds for K3 surfaces with ample line bundles.

-stability holds for abelian surfaces when L^2 > 13.

Provides criteria for stability depending on surface type and line bundle properties.

Abstract

Let X be a smooth projective surface over C and let L be a line bundle on X generated by its global sections. Let f:X-->P^r be the morphism associated to L and let T be the tangent bundle of P^r; we investigate the \mu-stability of f*T with respect to L when X is either a regular surface with p_g=0, a K3 surface or an abelian surface. In particular, we show that it is \mu-stable when X is K3 and L is ample and when X is abelian and L^2>13.