  Let G be a connected reductive group. In this paper we are studying the
invariant theory of symplectic G-modules. Our main result is that the invariant
moment map is equidimensional. We deduce that the categorical quotient is a
fibration over an affine space with rational generic fibers. Of particular
interest are those modules for which the generic orbit is coisotropic. We prove
that they are cofree. This result has been used in another paper
(math.SG/0505268) to classify all these modules. Our main tool is a symplectic
version of the local structure theorem.
