Victor Reiner, Alexander Woo, Alexander Yong
Published 2008-09-17, updated 2009-09-04Version 2
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.
Comments: 22 pages
Journal: Trans. Amer. Math. Soc. 363 (2011), 521-543
Pattern avoidance and fiber bundle structures on Schubert varieties
Smoothness of Schubert varieties via patterns in root systems
Combinatorics of semi-toric degenerations of Schubert varieties in type C
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