On fibers of algebraic invariant moment maps

In this paper we study some properties of fibers of the invariant moment map for a Hamiltonian action of a reductive group on an affine symplectic varieity. We prove that all fibers have equal dimension. Further, under some additional restrictions, we show that the quotients of fibers are irreducible normal schemes. This paper is an expanded version of Section 5 and Subsection 7.2 of AG/0612559v1.