English

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.

Keywords

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}
}

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22 pages