Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces

Chunyi Li; Xiaolei Zhao

Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces

Algebraic Geometry 2023-06-05 v2

Authors: Chunyi Li , Xiaolei Zhao

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.

Keywords

Bridgeland moduli spaces Poisson surfaces smoothness Poisson structures Bridgeland stable objects anti-canonical divisor

Cite

@article{arxiv.1612.02729,
  title  = {Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces},
  author = {Chunyi Li and Xiaolei Zhao},
  journal= {arXiv preprint arXiv:1612.02729},
  year   = {2023}
}

Comments

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 $K_X$

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