# The stability manifold of local orbifold elliptic quotients

## TL;DR

This paper explores the structure of the stability manifold associated with local orbifold quotients of elliptic curves, revealing a covering space relationship with the universal unfolding space of mirror singularities.

## Contribution

It provides a detailed description of a component of the stability manifold and its relation to mirror symmetry and McKay correspondence for surface singularities.

## Key findings

- Identified a component of the stability manifold as a covering space
- Connected the stability manifold to the universal unfolding space of mirror singularities
- Analyzed wall-crossing phenomena in the context of orbifold elliptic quotients

## Abstract

In this paper, we investigate the stability manifold of local models of orbifold quotients of elliptic curves. In particular, we describe a component of the stability manifold which maps as a covering space onto the universal unfolding space of the mirror singularity. The construction requires a detailed study of the McKay correspondence for $A_N$ surface singularities and a study of wall-crossing phenomena.