Presenting the cohomology of a schubert variety

Victor Reiner; Alexander Woo; Alexander Yong

doi:10.1090/S0002-9947-2010-05163-3

Presenting the cohomology of a schubert variety

Victor Reiner, Alexander Woo, Alexander Yong

School of Mathematics

Research output: Contribution to journal › Article › peer-review

13 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 language	English (US)
Pages (from-to)	521-543
Number of pages	23
Journal	Transactions of the American Mathematical Society
Volume	363
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-2010-05163-3
State	Published - Jan 2011

Keywords

Bigrassmannian
Cohomology presentation
Essential set
Schubert calculus
Schubert variety

Publisher link

10.1090/S0002-9947-2010-05163-3

Find It

Find It at U of M Libraries

Cite this

@article{b9fd97d3266e472a9677eca9ef8bca7e,

title = "Presenting the cohomology of a schubert variety",

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.",

keywords = "Bigrassmannian, Cohomology presentation, Essential set, Schubert calculus, Schubert variety",

author = "Victor Reiner and Alexander Woo and Alexander Yong",

year = "2011",

month = jan,

doi = "10.1090/S0002-9947-2010-05163-3",

language = "English (US)",

volume = "363",

pages = "521--543",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "1",

}

TY - JOUR

T1 - Presenting the cohomology of a schubert variety

AU - Reiner, Victor

AU - Woo, Alexander

AU - Yong, Alexander

PY - 2011/1

Y1 - 2011/1

N2 - 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.

AB - 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.

KW - Bigrassmannian

KW - Cohomology presentation

KW - Essential set

KW - Schubert calculus

KW - Schubert variety

UR - http://www.scopus.com/inward/record.url?scp=78651362801&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651362801&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-2010-05163-3

DO - 10.1090/S0002-9947-2010-05163-3

M3 - Article

AN - SCOPUS:78651362801

SN - 0002-9947

VL - 363

SP - 521

EP - 543

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 1

ER -

Presenting the cohomology of a schubert variety

Abstract

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this