论文标题
舒伯特品种中通用的圆环闭合的多项式多项式
Poincare polynomials of generic torus orbit closures in Schubert varieties
论文作者
论文摘要
众所周知，$ g/b $ a $的标志品种$ g/b $中的通用圆环的闭合是一个定位品种及其繁殖性多项式与Eulerian多项式一致。在本文中，我们研究了$ g/b $的舒伯特品种中通用圆环闭合的繁殖性多项式。当舒伯特品种中的通用圆环轨道闭合是光滑的时，它的繁殖多项式已知与欧拉多项式的一定概括一致。我们将此结果扩展到任意的通用圆环轨道闭合，这不一定是光滑的。
The closure of a generic torus orbit in the flag variety $G/B$ of type $A$ is known to be a permutohedral variety and its Poincare polynomial agrees with the Eulerian polynomial. In this paper, we study the Poincare polynomial of a generic torus orbit closure in a Schubert variety in $G/B$. When the generic torus orbit closure in a Schubert variety is smooth, its Poincare polynomial is known to agree with a certain generalization of the Eulerian polynomial. We extend this result to an arbitrary generic torus orbit closure which is not necessarily smooth.
