Stability of Kernel Sheaves on Del Pezzo Surfaces

TL;DR

This paper proves that kernel sheaves derived from sufficiently positive Gieseker stable sheaves on Del Pezzo surfaces are slope stable, marking a significant advancement in understanding stability of higher rank sheaves on surfaces.

Contribution

It introduces the first effective stability result for kernel sheaves linked to higher rank Gieseker stable sheaves on surfaces using Bridgeland stability techniques.

Findings

Kernel sheaves from positive Gieseker stable sheaves are slope stable.

First stability result for kernel sheaves associated to higher rank sheaves.

Establishes a new connection between Gieseker and slope stability on Del Pezzo surfaces.

Abstract

Using techniques from Bridgeland stability, we show the kernel sheaf associated to sufficiently positive Gieseker stable sheaf on a Del Pezzo surface is slope stable. This is the first effective stability result for kernel sheaves associated to higher rank sheaves on surfaces and the first stability result for kernel sheaves associated to Gieseker stable sheaves.