Determinants, even instantons and Bridgeland stability

TL;DR

This paper develops a systematic method to compute quiver regions for exceptional collections and applies it to prove Bridgeland stability of certain sheaves, including instantons, over projective spaces.

Contribution

It introduces a new systematic approach for calculating quiver regions and demonstrates Bridgeland stability for various instanton sheaves and bundles.

Findings

Bridgeland stability of 2-step complexes representing μ-stable sheaves.

Stability of even rank 2 instantons over ^3 and Q_3.

Description of moduli space near the main stability wall.

Abstract

We provide a systematic way of calculating a quiver region associated to a given exceptional collection, which as an application is used to prove that $\mu$-stable sheaves represented by $2$-step complexes are Bridgeland stable. In the later sections, we focus on the case of even rank $2$ instantons over $\mathbb{P}^3$ and $Q_3$ to prove that the instanton sheaves, instanton bundles and perverse instantons are Bridgeland stable and provide a description of the moduli space near their only actual wall.