Stability conditions for coherent systems on Integral Curves

TL;DR

This paper develops new stability conditions for coherent systems on integral curves using a three-parameter family of tilting-based pre-stability conditions, analyzing their qualification as true stability conditions and semistability of specific objects.

Contribution

It introduces a novel three-parameter family of stability conditions for coherent systems on integral curves and investigates their properties without relying on the support property.

Findings

Identified conditions under which pre-stability becomes true stability.

Analyzed semistability of torsion, free, and complete tilted systems.

Provided criteria for stability in the derived category context.

Abstract

We present stability conditions for the category of coherent systems on an integral curve. We define a three-parameter family of pre-stability conditions in its derived category using tilting, and we then investigate when these conditions qualify as true stability conditions. Additionally, we examine the semistability of specific objects under these conditions, namely: torsion, free, and complete tilted systems, without relying on the support property.