Presenting the cohomology of a Schubert variety
Combinatorics
2010-11-29 v2 Rings and Algebras
Abstract
We extend the short presentation due to [Borel '53] of the cohomology ring of a generalized flag manifold to a relatively short presentation of the cohomology of any of its Schubert varieties. Our result is stated in a root-system uniform manner by introducing the essential set of a Coxeter group element, generalizing and giving a new characterization of [Fulton '92]'s definition for permutations. Further refinements are obtained in type A.
Cite
@article{arxiv.0809.2981,
title = {Presenting the cohomology of a Schubert variety},
author = {Victor Reiner and Alexander Woo and Alexander Yong},
journal= {arXiv preprint arXiv:0809.2981},
year = {2010}
}
Comments
22 pages