Stability conditions on some families of Calabi-Yau threefolds via orbifolding

TL;DR

This paper demonstrates that certain families of Calabi-Yau threefolds, including the quintic mirror, can be equipped with Bridgeland stability conditions, especially when derived through orbifolding from known stable families.

Contribution

It establishes the existence of Bridgeland stability conditions on orbifolded Calabi-Yau threefolds, extending known cases to new families such as the quintic mirror.

Findings

Bridgeland stability conditions exist on orbifolded CY3s

The quintic mirror admits Bridgeland stability conditions

Stability conditions are preserved under orbifolding process

Abstract

We prove that families of Calabi-Yau threefolds (CY3's) admit Bridgeland stability conditions when they are obtained via orbifolding from a family of CY3's admitting Bridgeland stability conditions. In particular, we prove that the quintic mirror admits Bridgeland stability conditions.