  Suppose given an holomorphic and Hamiltonian action of a compact torus $T$ on
a polarized Hodge manifold $M$. Assume that the action lifts to the quantizing
line bundle, so that there is an induced unitary representation of $T$ on the
associated Hardy space. If in addition the moment map is nowhere zero, for each
weight $\boldsymbol{\nu}$ the $\boldsymbol{\nu}$-th isotypical component in the
Hardy space of the polarization is finite-dimensional. Assuming that the moment
map is transverse to the ray through $\boldsymbol{\nu}$, we give a gometric
interpretation of the isotypical components associated to the weights
$k\,\boldsymbol{\nu}$, $k\rightarrow +\infty$, in terms of certain polarized
orbifolds associated to the Hamiltonian action and the weight. These orbifolds
are generally not reductions of $M$ in the usual sense, but arise rather as
quotients of certain loci in the unit circle bundle of the polarization; this
construction generalizes the one of weighted projective spaces as quotients of
the unit sphere, viewed as the domain of the Hopf map.
