Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson   surfaces
  Let X be a projective smooth holomorphic Poisson surface, in other words, whose anti-canonical divisor is effective. We show that moduli spaces of certain Bridgeland stable objects on X are smooth. Moreover, we construct Poisson structures on these moduli spaces. 
Chunyi Li and Xiaolei Zhao
math.AG