Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces
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Let X be a projective smooth holomorphic Poisson surface, in other words, whose anti-canonical bundle 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.
KeywordsPoisson structure Stability condition Moduli of complexes
The authors are greatly indebted to Arend Bayer for his tremendous assistance. In particular, Lemmas 3 and 4 are suggested by him, and first appear in his talk in the workshop “Derived Categories and Moduli Spaces” at University of Stavanger. We are grateful to Wanmin Liu and Emanuele Macrì for helpful conversations. We would like to thank the anonymous referee for many helpful comments on the exposition. Chunyi Li is supported by ERC starting Grant No. 337039 “WallXBirGeom”.
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