Stability conditions and the $A_2$ quiver

TL;DR

This paper characterizes the space of stability conditions on the derived category of Ginzburg algebras linked to the $A_2$ quiver, revealing connections to Frobenius-Saito structures and singularity theory.

Contribution

It provides a detailed description of stability condition spaces for Ginzburg algebras associated with the $A_2$ quiver, highlighting their relation to singularity unfolding structures.

Findings

Explicit description of stability spaces for all $n \\geq 2$

Identification of links to Frobenius-Saito structures

Insights into the geometry of derived categories and singularities

Abstract

For each integer $n\geq2$ we describe the space of stability conditions on the derived category of the $n$-dimensional Ginzburg algebra associated to the $A_2$ quiver. The form of our results points to a close relationship between these spaces and the Frobenius-Saito structure on the unfolding space of the $A_2$ singularity.