Toric matrix Schubert varieties and their polytopes
Toric matrix Schubert varieties and their polytopes
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环面矩阵舒伯特簇及其多胞形
DOI：
10.1090/proc/13152
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Karola Mészáros
中科院分区：
文献类型：
--
作者：
Laura Escobar;Karola Mészáros
给定一个矩阵Schubert变数$OVERLINE{X_\pi}$，它可以记为$\OVERLINE{X_\pi}=Y_\pi\Times\mathbb{C}^q$(其中$q$是最大可能的)。我们刻画了$Y_{\pi}$是环面的(关于$(\mathbb{C}^*)^{2n-1}$-作用)，并研究了它的射影的相关多面体$\Phi(\mathbb{P}(Y_\pi))$。我们构造了$\Phi(\mathbb{P}(Y_\pi))$的正则三角剖分，证明了它是一族子词复合体的几何实现。子词复合体是Knutson和Miller在2004年提出的，他们还证明了子词复合体与球或球体是同胚的，并提出了子词复合体的多面化实现问题。
Given a matrix Schubert variety $\overline{X_\pi}$, it can be written as $\overline{X_\pi}=Y_\pi\times \mathbb{C}^q$ (where $q$ is maximal possible). We characterize when $Y_{\pi}$ is toric (with respect to a $(\mathbb{C}^*)^{2n-1}$-action) and study the associated polytope $\Phi(\mathbb{P}(Y_\pi))$ of its projectivization. We construct regular triangulations of $\Phi(\mathbb{P}(Y_\pi))$ which we show are geometric realizations of a family of subword complexes. Subword complexes were introduced by Knutson and Miller in 2004, who also showed that they are homeomorphic to balls or spheres and raised the question of their polytopal realizations.
子词复合体、簇复合体和广义多关联面体
影响因子：
0.8
作者：
Cesar Ceballos;Jean-Philippe Labbé;Christian Stump
通讯作者：
Christian Stump
$$A$$A 类型子词复合体和 3 阶多关联面体的粉丝实现
影响因子：
0.8
作者：
Nantel Bergeron;Cesar Ceballos;Jean-Philippe Labbé
通讯作者：
Jean-Philippe Labbé