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Presenting the cohomology of a Schubert variety

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.

preprint2009arXivOpen access
Victor ReinerAlexander WooAlexander Yong
math.COmath.RA
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Victor ReinerAlexander WooAlexander Yong

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