Deformations of holomorphic Poisson manifolds
Differential Geometry
2011-05-25 v1 Algebraic Geometry
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.
Cite
@article{arxiv.1105.4775,
title = {Deformations of holomorphic Poisson manifolds},
author = {Nigel Hitchin},
journal= {arXiv preprint arXiv:1105.4775},
year = {2011}
}
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32 pages