Presenting the cohomology of a Schubert variety

Reiner, Victor; Woo, Alexander; Yong, Alexander

doi:10.1090/S0002-9947-2010-05163-3

Presenting the cohomology of a Schubert variety
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by Victor Reiner, Alexander Woo and Alexander Yong PDF

Trans. Amer. Math. Soc. 363 (2011), 521-543 Request permission

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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