A short proof of the deformation property of Bridgeland stability conditions

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.

arXiv comment14 pages, 6 figures. v2: Exposition overhauled. Addressed inaccuracy (thanks to Martin Gulbrandsen for pointing it out) in treating the topology. v3: addressed referee comments improving the exposition. To appear in Math. Annalen