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摘要翻译：
局部化是一种拓扑技术，它允许我们根据不动点上的局部数据进行全局等变计算。例如，我们可以通过求和每个不动点上的积分来计算全局积分。或者，如果我们知道全局积分为零，我们就得出局部积分之和为零的结论。这常常把拓扑问题变成组合问题，反之亦然。这篇说明性文章以发生在辛几何和代数几何以及组合理论和表示理论的十字路口的几个局部化实例为特色。这些例子主要来自辛范畴，特别关注toric变体。本着2006年在大阪城市大学举行的国际复圈拓扑会议的精神，这次博览会的主要目标是展示辛几何中出现的复圈技术。
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英文标题：
《Act globally, compute locally: group actions, fixed points, and
localization》
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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：
Localization is a topological technique that allows us to make global equivariant computations in terms of local data at the fixed points. For example, we may compute a global integral by summing integrals at each of the fixed points. Or, if we know that the global integral is zero, we conclude that the sum of the local integrals is zero. This often turns topological questions into combinatorial ones and vice versa. This expository article features several instances of localization that occur at the crossroads of symplectic and algebraic geometry on the one hand, and combinatorics and representation theory on the other. The examples come largely from the symplectic category, with particular attention to toric varieties. In the spirit of the 2006 International Conference on Toric Topology at Osaka City University, the main goal of this exposition is to exhibit toric techniques that arise in symplectic geometry.
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PDF链接：
https://arxiv.org/pdf/0710.5295
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