A short proof of the deformation property of Bridgeland stability   conditions
  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. 
Arend Bayer
math.AG