W-translated Schubert divisors and transversal intersections

Dong Seon Hwang; Hwayoung Lee; Jae Hyouk Lee; Changzheng Li

doi:10.1007/s11425-021-1940-6

W-translated Schubert divisors and transversal intersections

Dong Seon Hwang, Hwayoung Lee, Jae Hyouk Lee, Changzheng Li

Department of Mathematics

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

Abstract

We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety Fℓn1,…,nk;n via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimensions intersect transversally up to translation by Weyl group elements, and verify it in various cases, including the complex Grassmannian Gr(2, n) and the complete flag variety Fℓ_1,2,3,4.

Original language	English
Pages (from-to)	1997-2018
Number of pages	22
Journal	Science China Mathematics
Volume	65
Issue number	10
DOIs	https://doi.org/10.1007/s11425-021-1940-6
State	Published - Oct 2022

Bibliographical note

Publisher Copyright:
© 2022, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

14M15
14M25
14N15
Gelfand-Cetlin polytope
W-translated Schubert varieties
flag varieties
toric degeneration
transversal intersection

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10.1007/s11425-021-1940-6

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title = "W-translated Schubert divisors and transversal intersections",

abstract = "We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety Fℓn1,…,nk;n via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimensions intersect transversally up to translation by Weyl group elements, and verify it in various cases, including the complex Grassmannian Gr(2, n) and the complete flag variety Fℓ1,2,3,4.",

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author = "Hwang, {Dong Seon} and Hwayoung Lee and Lee, {Jae Hyouk} and Changzheng Li",

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AU - Hwang, Dong Seon

AU - Lee, Hwayoung

AU - Lee, Jae Hyouk

AU - Li, Changzheng

PY - 2022/10

Y1 - 2022/10

N2 - We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety Fℓn1,…,nk;n via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimensions intersect transversally up to translation by Weyl group elements, and verify it in various cases, including the complex Grassmannian Gr(2, n) and the complete flag variety Fℓ1,2,3,4.

AB - We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety Fℓn1,…,nk;n via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimensions intersect transversally up to translation by Weyl group elements, and verify it in various cases, including the complex Grassmannian Gr(2, n) and the complete flag variety Fℓ1,2,3,4.

KW - 14M15

KW - 14M25

KW - 14N15

KW - Gelfand-Cetlin polytope

KW - W-translated Schubert varieties

KW - flag varieties

KW - toric degeneration

KW - transversal intersection

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DO - 10.1007/s11425-021-1940-6

M3 - Article

AN - SCOPUS:85128483155

SN - 1674-7283

VL - 65

SP - 1997

EP - 2018

JO - Science China Mathematics

JF - Science China Mathematics

IS - 10

ER -

W-translated Schubert divisors and transversal intersections

Abstract

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Keywords

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