Bruhat order, smooth Schubert varieties, and hyperplane arrangements
Combinatorics
2007-09-21 v1
Abstract
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.
Cite
@article{arxiv.0709.3259,
title = {Bruhat order, smooth Schubert varieties, and hyperplane arrangements},
author = {Suho Oh and Alexander Postnikov and Hwanchul Yoo},
journal= {arXiv preprint arXiv:0709.3259},
year = {2007}
}
Comments
14 pages, 2 figures