Generic torus orbit closures in Schubert varieties
Generic torus orbit closures in Schubert varieties
复制标题
舒伯特簇中的通用环面轨道闭合
DOI：
10.1016/j.jcta.2019.105143
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Eunjeong Lee and Mikiya Masuda
中科院分区：
文献类型：
--
作者：
Eunjeong Lee;Mikiya Masuda;and Seonjeong Park;Eunjeong Lee and Mikiya Masuda
已知a - n - 1型旗型G/B中的一般环面轨道闭合是一个多面体型，并得到了充分的研究。本文在Schubert变换X w （w∈S n）中引入了一般环面轨道的概念，并研究了它的闭包Y w。我们在Y w的扇形中识别了一个不动点uB （u≤w）对应的极大锥，并将一个图Γ w (u)关联到每个u≤w上，证明了Y w在uB上是光滑的当且仅当Γ w (u)是森林。我们还为每个w引入了一个多项式a w (t)，当w是S n的最长元素时，它与欧拉多项式一致，并证明了当Y w是光滑的时，Y w的poincar<s:1>多项式与a w （t2）一致。
The closure of a generic torus orbit in the flag variety G/B of type A n− 1 is known to be a permutohedral variety and well studied. In this paper we introduce the notion of a generic torus orbit in the Schubert variety X w (w∈ S n) and study its closure Y w. We identify the maximal cone in the fan of Y w corresponding to a fixed point uB (u≤ w), associate a graph Γ w (u) to each u≤ w, and show that Y w is smooth at uB if and only if Γ w (u) is a forest. We also introduce a polynomial A w (t) for each w, which agrees with the Eulerian polynomial when w is the longest element of S n, and show that the Poincaré polynomial of Y w agrees with A w (t 2) when Y w is smooth.