Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces

Abstract

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.Comment: We would like to thank Sergey Mozgovoy for pointing out a mistake in the first and journal version of this paper. Our result only holds for $H$ that is numerically parallel to $K_X