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Deformations of holomorphic Poisson manifolds

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.

preprint2011arXivOpen access
Nigel Hitchin
math.AGmath.DG
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Nigel Hitchin

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