Delzant空间的约化相空间与环面簇协调
Reduced phase space and toric variety coordinatizations of Delzant spaces
摘要：
本文从辛几何的观点出发，描述了约化相空间的Delzant空间的自然坐标化，并给出了坐标变换的显式公式。对于Delzant多面体上环面作用的每一个不动点，我们都有Delzant空间中包含该不动点的开胞的极大坐标化。这个胞腔等于Delzant空间作为复曲面簇的一种自然坐标化的定义域（复代数几何观点），并给出了复曲面簇坐标在约化相空间坐标下的显式表达式.我们使用的考虑在最大的坐标邻域给简单的证明的一些基本事实的Delzant空间，作为一个减少相空间，并作为一个复曲面品种。这些可以被看作是协调的第一个应用，并有助于使演示更加独立。
英文摘要：
In this note we describe the natural coordinatizations of a Delzant space defined as a reduced phase space (symplectic geometry view-point) and give explicit formulas for the coordinate transformations. For each fixed point of the torus action on the Delzant polytope, we have a maximal coordinatization of an open cell in the Delzant space which contains the fixed point. This cell is equal to the domain of definition of one of the natural coordinatizations of the Delzant space as a toric variety (complex algebraic geometry view-point), and we give an explicit formula for the toric variety coordinates in terms of the reduced phase space coordinates. We use considerations in the maximal coordinate neighborhoods to give simple proofs of some of the basic facts about the Delzant space, as a reduced phase space, and as a toric variety. These can be viewed as a first application of the coordinatizations, and serve to make the presentation more self-contained.
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