Suppose given a 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 ν the ν-th isotypical component in the Hardy space of the polarization is finite-dimensional. Assuming that the moment map is transverse to the ray through ν, we give a geometric interpretation of the isotypical components associated to the weights $k\mathit{\nu }$, $k\to +\infty$, 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.

假设给定一个紧致环面T在极化霍奇流形M上的全纯和哈密顿作用。假设动作提升到量化线丛，因此在相关的哈代空间上存在T的诱导幺正表示。如果除了当下地图无处零，对于每个权重ν的ν在偏振Hardy空间第isotypical组分是有限维。假设矩图通过ν与射线垂直，我们给出与权重相关的同型分量的几何解释$克\mathit{\nu }$, $克\to +\infty$，就与哈密顿作用和权重相关的某些极化轨道而言。这些轨道通常不是通常意义上的M 的减少，而是作为偏振单位圆束中某些位点的商出现的；这种构造将加权投影空间之一概括为单位球体的商，被视为 Hopf 映射的域。