A Propos de l'Existence de Fibr\'es Stables sur les Surfaces

TL;DR

This paper proves the existence of stable vector bundles with specified properties on any polarized smooth projective surface over characteristic zero, given sufficiently large second Chern class.

Contribution

It establishes the existence of stable bundles with arbitrary first Chern class and large second Chern class on all polarized smooth projective surfaces in characteristic zero.

Findings

Existence of stable bundles proven for all polarized surfaces

Stable bundles with arbitrary first Chern class constructed

Results hold in characteristic zero

Abstract

We prove the existence (in characteristic 0) on every polarized (smooth, projective and connected) surface of stable bundles of rank $r\geq 2$, arbitrary first Chern class and large enough $c_2$.