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Mosc. Math. J., 2012, Volume 12, Number 3, Pages 567–591 (Mi mmj458)  

This article is cited in 8 scientific papers (total in 8 papers)

Deformations of holomorphic Poisson manifolds

Nigel Hitchin

Mathematical Institute, 24-29 St Giles, Oxford OX1 3LB, UK

Abstract: An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in particular the Hilbert schemes of the projective plane and show that a generic deformation is determined by two parameters — an elliptic curve and a translation on it.

Key words and phrases: Poisson manifold, Kodaira–Spencer class, deformation of complex structure, Hilbert scheme, exceptional divisor.

DOI: https://doi.org/10.17323/1609-4514-2012-12-3-567-591

Full text: http://www.ams.org/.../abst12-3-2012.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 32G05, 53D17, 53D18
Received: May 12, 2011
Language:

Citation: Nigel Hitchin, “Deformations of holomorphic Poisson manifolds”, Mosc. Math. J., 12:3 (2012), 567–591

Citation in format AMSBIB
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\by Nigel~Hitchin
\paper Deformations of holomorphic Poisson manifolds
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 3
\pages 567--591
\mathnet{http://mi.mathnet.ru/mmj458}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-3-567-591}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3024823}
\zmath{https://zbmath.org/?q=an:06126187}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Grandini D., Poon Ya.-S., Rolle B., “Differential Gerstenhaber Algebras of Generalized Complex Structures”, Asian J. Math., 18:2 (2014), 191–218  crossref  mathscinet  zmath  isi  scopus
    2. Grantcharov G., Hernandez-Vazquez L., “Poisson Structures on Twistor Spaces of Hyperkahler and Hkt Manifolds”, J. Geom. Phys., 91 (2015), 131–140  crossref  zmath  isi  elib  scopus
    3. Apostolov V., Bailey M., Dloussky G., “From Locally Conformally Kahler To Bi-Hermitian Structures on Non-Kahler Complex Surfaces”, Math. Res. Lett., 22:2 (2015), 317–336  crossref  zmath  isi  elib
    4. Zh. Chen, A. Fino, Ya.-S. Poon, “Holomorphic Poisson structure and its cohomology on nilmanifolds”, Differ. Geom. Appl., 44 (2016), 144–160  crossref  zmath  isi  scopus
    5. Chunyi Li, “Deformations of the Hilbert scheme of points on a del Pezzo surface”, Mosc. Math. J., 17:2 (2017), 291–321  mathnet  mathscinet
    6. Ya. S. Poon, J. Simanyi, “A Hodge-type decomposition of holomorphic Poisson cohomology on nilmanifolds”, Complex Manifolds, 4:1 (2017), 137–154  crossref  mathscinet  zmath  isi  scopus
    7. Hua Zh., Polishchuk A., “Shifted Poisson Structures and Moduli Spaces of Complexes”, Adv. Math., 338 (2018), 991–1037  crossref  mathscinet  zmath  isi  scopus
    8. Li Ch., Zhao X., “The Minimal Model Program For Deformations of Hilbert Schemes of Points on the Projective Plane”, Algebraic Geom., 5:3 (2018), 328–358  crossref  mathscinet  zmath  isi  scopus
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