The modular curve as the space of stability conditions of a CY3 algebra

TL;DR

This paper establishes a deep connection between the space of stability conditions on a CY3 triangulated category and the universal cover of a bundle over the moduli space of elliptic curves, revealing geometric insights into CY3 categories.

Contribution

It demonstrates that a component of the stability condition space for a CY3 category generated by A_2 spherical objects is isomorphic to a universal cover of a holomorphic differential bundle over elliptic moduli space.

Findings

Identifies the stability condition space with a universal cover of a differential bundle.

Connects CY3 categories with elliptic curve moduli space geometry.

Provides a geometric model for stability conditions in CY3 categories.

Abstract

We prove that a connected component of the space of stability conditions of a CY3 triangulated category generated by an A_2 collection of 3-spherical objects is isomorphic to the universal cover of the C^*-bundle of non-zero holomorphic differentials on the moduli space of elliptic curves.