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arXiv · 0809.2981

Presenting the cohomology of a Schubert variety

Victor Reiner·Alexander Woo·Alexander Yong
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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.

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Victor Reiner, Alexander Woo, Alexander Yong. 2009-09-04. Presenting the cohomology of a Schubert variety. https://arxiv.org/abs/0809.2981

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