Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces

TL;DR

This paper demonstrates the smoothness of certain Bridgeland moduli spaces on Poisson surfaces and constructs compatible Poisson structures, advancing the understanding of their geometric and algebraic properties.

Contribution

It establishes the smoothness of Bridgeland moduli spaces on Poisson surfaces and introduces Poisson structures on these moduli spaces, linking stability conditions with Poisson geometry.

Findings

Moduli spaces are smooth for certain Bridgeland stable objects.

Poisson structures can be constructed on these moduli spaces.

Results connect stability conditions with Poisson geometry on 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.