  Suppose given a linearized action on a polarized complex projective manifold
(M,L), and assume that the stable locus is non-empty. We study the leading
asymptotics of the dimension of the equivariant summands appearing in the space
of global sections of high powers of L. We use Kirwan resolutions and an
elementary algebro-geometric argument to reduce the problem to the case of
non-singular actions (that is, actions for which the stable and semistable loci
coincide and are non-empty).
