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摘要翻译：
本文利用复圈几何研究了Grassmannian(Gr_{kn}）_{\geq0}的全非负部分的拓扑。这是一个单元复合体，它的单元Delta_G可以用平面二分图G的组合来参数化，每个单元Delta_G都对应一个多面体P(G)。多边形P(G)类似于著名的Birkhoff多边形，我们用G的匹配和匹配的并来描述它们的面格。我们还证明了多边形P(G)与拟阵多边形之间的密切联系。然后我们利用P(G)的数据定义了一个相关的toric变量X_g。利用我们的技术证明了(Gr_{kn}）_{\geq0}的胞分解是CW复形，进而证明了(Gr_{kn}）_{\geq0}的每个胞闭包的欧拉特征为1。
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英文标题：
《Matching polytopes, toric geometry, and the non-negative part of the
Grassmannian》
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作者：
Alexander Postnikov, David Speyer, Lauren Williams
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最新提交年份：
2008
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分类信息：
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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一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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英文摘要：
In this paper we use toric geometry to investigate the topology of the totally non-negative part of the Grassmannian (Gr_{kn})_{\geq 0}. This is a cell complex whose cells Delta_G can be parameterized in terms of the combinatorics of plane-bipartite graphs G. To each cell Delta_G we associate a certain polytope P(G). The polytopes P(G) are analogous to the well-known Birkhoff polytopes, and we describe their face lattices in terms of matchings and unions of matchings of G. We also demonstrate a close connection between the polytopes P(G) and matroid polytopes. We then use the data of P(G) to define an associated toric variety X_G. We use our technology to prove that the cell decomposition of (Gr_{kn})_{\geq 0} is a CW complex, and furthermore, that the Euler characteristic of the closure of each cell of (Gr_{kn})_{\geq 0} is 1.
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PDF链接：
https://arxiv.org/pdf/0706.2501
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