Deformations of Holomorphic Poisson Manifolds

  title={Deformations of Holomorphic Poisson Manifolds},
  author={Nigel Hitchin},
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.