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摘要翻译：
本文描述了定义为约化相空间（辛几何视点）的Delzant空间的自然坐标，并给出了坐标变换的显式公式。对于环面作用在Delzant多面体上的每个不动点，我们在包含该不动点的Delzant空间中有一个开胞的极大协调。该单元等于Delzant空间的一个自然配位点的定义域（复代数几何视点），并给出了用简化相空间坐标表示该配位点坐标的显式公式。我们使用极大坐标邻域中的考虑来简单地证明关于Delzant空间的一些基本事实，作为一个约化相空间，作为一个toric变体。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。
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英文标题：
《Reduced phase space and toric variety coordinatizations of Delzant
spaces》
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作者：
J.J. Duistermaat and A. Pelayo
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Symplectic Geometry 辛几何
分类描述：Hamiltonian systems, symplectic flows, classical integrable systems
哈密顿系统，辛流，经典可积系统
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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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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PDF链接：
https://arxiv.org/pdf/0704.0430
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