Almost Homogeneous Poisson Spaces

Details Almost Homogeneous Poisson Spaces Almost Homogeneous Poisson Spaces

2003-07-10

arxiv.org/abs/math/0307135v1

Mathematics

Symplectic Geometry

19 pages

Scientific paper

We prove that any holomorphic Poisson manifold has an open symplectic leaf which is a pseudo-K\"ahler submanifold, and we define an obstruction to study the equivariance of momentum map for tangential Poisson action. Some properties of almost homogeneous Poisson manifolds are studied and we show that any compact symplectic Poisson homogeneous space is a torus bundle over a dressing orbit.

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