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Cohomology of Smooth Schubert Varieties in Partial Flag Manifolds
Author(s) -
Gasharov V.,
Reiner V.
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003605
Subject(s) - flag (linear algebra) , mathematics , generalized flag variety , cohomology ring , pure mathematics , iterated function , schubert polynomial , schubert calculus , cohomology , schubert variety , class (philosophy) , chern class , grassmannian , algebra over a field , equivariant cohomology , lie group , mathematical analysis , computer science , artificial intelligence
The fact that smooth Schubert varieties in partial flag manifolds are iterated fiber bundles over Grassmannians is used to give a simple presentation for their integral cohomology ring, generalizing Borel's presentation for the cohomology of the partial flag manifold itself. More generally, such a presentation is shown to hold for a larger class of subvarieties of the partial flag manifolds (which are called subvarieties defined by inclusions). The Schubert varieties which lie within this larger class are characterized combinatorially by a pattern avoidance condition.