Determinants, even instantons and Bridgeland stability

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.