与量子化Hamilton环面作用量相关的极化轨道折叠
Polarized orbifolds associated to quantized Hamiltonian torus actions
摘要：
设给定紧环面$T$在极化Hodge流形$M$上的一个全纯作用和一个Hamilton作用.假设动作提升到量化线丛，使得在相关的Hardy空间上存在$T$的诱导酉表示。此外，如果矩映射无处为零，则对于每个权重$\boldsymbolν$，极化的Hardy空间中的第$\boldsymbolν$同构分量是有限维的。假设矩映射是横向的射线通过$\boldsymbolν$，我们给出了几何解释的同构组件相关的权重$k\,\boldsymbolν$，$k\rightarrow +\infty$，在某些偏振orbifolds相关的哈密顿作用和重量。这些轨道折叠一般不是通常意义上的$M$的约化，而是作为极化的单位圆丛中某些轨迹的导数而产生的;这种构造将加权射影空间的一个推广为单位球面的导数，单位球面被视为霍普夫映射的域。
英文摘要：
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 $\boldsymbolν$ the $\boldsymbolν$-th isotypical component in the Hardy space of the polarization is finite-dimensional. Assuming that the moment map is transverse to the ray through $\boldsymbolν$, we give a gometric interpretation of the isotypical components associated to the weights $k\,\boldsymbolν$, $k\rightarrow +\infty$, 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.
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