Presenting the cohomology of a schubert variety

Victor Reiner, Alexander Woo, Alexander Yong

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)521-543
Number of pages23
JournalTransactions of the American Mathematical Society
Volume363
Issue number1
DOIs
StatePublished - Jan 2011

Keywords

  • Bigrassmannian
  • Cohomology presentation
  • Essential set
  • Schubert calculus
  • Schubert variety

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