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摘要翻译：
这些注释伴随着关于辛（和其他）商的拓扑的讲座。其目的有两个：第一，宣传辛范畴的计算容易；其次给出了加权射影空间的一些新的计算方法。我们首先简要地阐述了在辛范畴中轨道是如何产生的，并讨论了用来理解它们的拓扑结构的技术。然后，我们证明了这些结果如何用于计算阿贝尔辛约化的Chen-阮轨道上同调环。我们通过比较与加权射影空间相关的几个环得出结论。我们直接进行这些计算，避免提到堆叠扇形或标记矩多面体。
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英文标题：
《Orbifold cohomology of abelian symplectic reductions and the case of
weighted projective spaces》
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作者：
Tara S. Holm
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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：
These notes accompany a lecture about the topology of symplectic (and other) quotients. The aim is two-fold: first to advertise the ease of computation in the symplectic category; and second to give an account of some new computations for weighted projective spaces. We start with a brief exposition of how orbifolds arise in the symplectic category, and discuss the techniques used to understand their topology. We then show how these results can be used to compute the Chen-Ruan orbifold cohomology ring of abelian symplectic reductions. We conclude by comparing the several rings associated to a weighted projective space. We make these computations directly, avoiding any mention of a stacky fan or of a labeled moment polytope.
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PDF链接：
https://arxiv.org/pdf/0704.0257
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