Math. Z. https://doi.org/10.1007/s00209-018-2090-5 Mathematische Zeitschrift Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces 1 2 Chunyi Li · Xiaolei Zhao Received: 24 June 2017 / Accepted: 2 February 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract 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. Keywords Poisson structure · Stability condition · Moduli of complexes 1 Introduction It is proved by Mukai in  that the moduli space of stable sheaves on an abelian or a projective K3 surface is smooth and has a natural symplectic structure. This construction has been generalized in two directions. On the one hand, the symplectic structure can be generalized to (holomorphic) Poisson structures. In the paper , the author showed that a Poisson structure on the surface will naturally determine an antisymmetric bivector ﬁeld on the moduli space of stable sheaves. Bottacin  then proved that such a bivector ﬁeld satisﬁes the closure condition and endows the moduli space with a natural Poisson structure. On the
Mathematische Zeitschrift – Springer Journals
Published: Jun 5, 2018
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