Derived category of coherent systems on curves and stability conditions

TL;DR

This paper explores the stability conditions on the derived category of coherent systems on a smooth projective curve, linking the stability manifold to the curve's Brill--Noether theory.

Contribution

It describes an open locus of Bridgeland stability conditions and connects the stability manifold with the Brill--Noether theory of the curve.

Findings

Identifies an open locus of stability conditions on the derived category

Shows the stability manifold detects Brill--Noether theory

Provides new insights into the geometry of coherent systems

Abstract

Let $C$ be a smooth projective curve of genus $g>0$. We describe an open locus of Bridgeland stability conditions on the bounded derived category of coherent systems on $C$, and show that stability manifold detects the Brill--Noether theory of the curve.