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.
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