Polarized orbifolds associated to quantized Hamiltonian torus actions

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