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COHOMOLOGY OF SMOOTH SCHUBERT VARIETIES IN PARTIAL FLAG MANIFOLDS

Published online by Cambridge University Press:  24 March 2003

V. GASHAROV  and
V. REINER
V. GASHAROV
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, [email protected]
V. REINER
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, [email protected]
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Abstract

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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 66 , Issue 3 , December 2002 , pp. 550 - 562
Copyright
© The London Mathematical Society, 2002

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