Asymptotic slopes and strong semistability on surfaces

TL;DR

This paper investigates the behavior of asymptotic slopes of strongly semistable vector bundles on surfaces, establishing links with restriction theorems and providing new criteria for strong semistability.

Contribution

It introduces an equivalent criterion for strong semistability based on asymptotic slopes, under specific conditions on the surface and bundle.

Findings

Established a connection between asymptotic slopes and restriction theorems.

Provided an equivalent criterion for strong semistability.

Analyzed asymptotic slopes on smooth projective surfaces.

Abstract

In this article we study asymptotic slopes of strongly semistable vector bundles on a smooth projective surface. A connection between asymptotic slopes and strong restriction theorem of a strongly semistable vector bundle is shown. We also give an equivalent criterion of strong semistability of a vector bundle in terms of its asymptotic slopes under some assumptions on the surface and on the bundle.