A short proof of the deformation property of Bridgeland stability conditions

TL;DR

This paper provides a concise proof of the deformation property of Bridgeland stability conditions, confirming they form a complex manifold by showing small deformations of the central charge correspond uniquely to deformations of the stability condition.

Contribution

It offers a short, direct proof of the deformation property, strengthening the understanding of the structure of Bridgeland stability conditions.

Findings

Confirmed that Bridgeland stability conditions form a complex manifold.

Established a strong version of the deformation property.

Provided a simplified proof technique for the deformation property.

Abstract

The key result in the theory of Bridgeland stability conditions is the property that they form a complex manifold. This comes from the fact that given any small deformation of the central charge, there is a unique way to correspondingly deform the stability condition. We give a short direct proof of a strong version of this deformation property.