On quantum cohomology rings of partial flag varieties
type: Item
instance of: scholarly article
title: On quantum cohomology rings of partial flag varieties
zbMATH Open document ID: 0969.14039
DOI: 10.1215/S0012-7094-99-09815-0
author: Ionuţ Ciocan-Fontanine
published in: Duke Mathematical Journal
publication date: 2000-03-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/9710213
review text: In this article a unified description of the structure of the small cohomology rings for all projective homogeneous spaces \(SL_n(\mathbb C)/P\) (with \(P\) a parabolic subgroup) is given. First the results on the classical cohomology rings are recalled. Then the algebraic structure of the quantum cohomology ring is studied. Important results are the general quantum versions of the Giambelli and Pieri formulas of the classical cohomology (classical Schubert calculus). They are obtained via geometric computations of certain Gromov-Witten invariants, which are realized as intersection numbers on hyperquot schemes.
reviewed by: M. Schlichenmaier
Mathematics Subject Classification ID: 14N35
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 14N15
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 53D45
zbMATH DE Number: 1425230
zbMATH Keywords: quantum cohomology
zbMATH Keywords: Gromov-Witten invariants
zbMATH Keywords: Schubert calculus
zbMATH Keywords: small cohomology rings
zbMATH Keywords: homogeneous spaces
zbMATH Keywords: Pieri formulas
MaRDI profile type: Publication
arXiv ID: math/9710213
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OpenAlex ID: W1937264024
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description: scientific article