Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 437–447 | Cite as

Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces

  • Chunyi Li
  • Xiaolei ZhaoEmail author


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.


Poisson 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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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK
  2. 2.Department of MathematicsNortheastern UniversityBostonUSA

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