Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces

Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces 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 [13] 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 [14], 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 [5] then proved that such a bivector field satisfies the closure condition and endows the moduli space with a natural Poisson structure. On the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
D.O.I.
10.1007/s00209-018-2090-5
Publisher site
See Article on Publisher Site

Abstract

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 [13] 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 [14], 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 [5] then proved that such a bivector field satisfies the closure condition and endows the moduli space with a natural Poisson structure. On the

Journal

Mathematische ZeitschriftSpringer Journals

Published: Jun 5, 2018

References

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