Algebraic Hamiltonian Actions
نویسنده
چکیده
In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X . We study the quotient morphism μG,X//G : X//G → g//G of the moment map μG,X : X → g. We prove that for a wide class of Hamiltonian actions (including, for example, actions on generically symplectic varieties) all fibers of the morphism μG,X//G have the same dimension. We also study the ”Stein factorization” of μG,X//G. Namely, let CG,X denote the spectrum of the integral closure of μ∗G,X(K[g] ) in K(X). We investigate the structure of the g//G-scheme CG,X . Our results partially generalize those obtained by F. Knop for the actions on cotangent bundles and symplectic vector spaces.
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تاریخ انتشار 2009