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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Presenting the cohomology of a Schubert variety

Authors: Victor Reiner, Alexander Woo and Alexander Yong
Journal: Trans. Amer. Math. Soc. 363 (2011), 521-543
MSC (2000): Primary 14M15, 14N15
Published electronically: August 13, 2010
MathSciNet review: 2719692
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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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Additional Information

Victor Reiner
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Alexander Woo
Affiliation: Department of Mathematics, Statistics, and Computer Science, Saint Olaf College, Northfield, Minnesota 55057

Alexander Yong
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

Keywords: Schubert calculus, Schubert variety, cohomology presentation, bigrassmannian, essential set
Received by editor(s): November 27, 2008
Received by editor(s) in revised form: June 29, 2009
Published electronically: August 13, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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