论文标题
与量化的哈密顿圆环动作相关的偏光轨道
Polarized orbifolds associated to quantized Hamiltonian torus actions
论文作者
论文摘要
假设鉴于在两极分化的霍奇歧管$ m $上进行紧凑的圆环$ t $的全态和汉密尔顿动作。假设该动作将升至量化线捆绑包，以便在相关的Hardy空间上有$ t $的统一表示。如果此外，如果矩映射无处可零，则对于每个重量$ \boldsymbolν$ $ \boldsymbolν$ - th $ th在偏光范围内的同种型组件是有限维度的。假设Moment Map通过$ \boldsymbolν$横向到射线，我们就与重量相关的同种型组件进行了高度解释。在通常的意义上，这些Orbifold通常不是$ m $的减少，而是作为两极分化单元圆圈中某些基因座的商而出现的。这种结构将加权投影空间之一概括为单位球的商，被视为Hopf地图的域。
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.
