Presenting the cohomology of a Schubert variety

Details Presenting the cohomology of a Schubert variety Presenting the cohomology of a Schubert variety

2008-09-17

arxiv.org/abs/0809.2981v2

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

Mathematics

Combinatorics

22 pages

Scientific paper

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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