Bruhat order, smooth Schubert varieties, and hyperplane arrangements

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:115

Article

Oh, Suho¹  Postnikov, Alexander¹  Yoo, Hwanchul¹ 

[1] MIT, Dept Math, Cambridge, MA 02139 USA

关键词: flag manifold;    Schubert varieties;    smoothness;    hyperplane arrangements;    Bruhat order;    Poincare polynomials;    chordal graphs;    perfect elimination ordering;   

DOI  :  10.1016/j.jcta.2008.01.003

来源: Elsevier

【 摘 要 】

The aim of this article is to link Schubert varieties in the flag manifold with hyperplane arrangements. For a permutation, we construct a certain graphical hyperplane arrangement. We show that the generating function for regions of this arrangement coincides with the Poincare polynomial of the corresponding Schubert variety if and only if the Schubert variety is smooth. We give an explicit combinatorial formula for the Poincare polynomial. Our main technical tools are chordal graphs and perfect elimination orderings. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free