The connectedness of hessenberg varieties

Martha Precup

doi:10.1016/j.jalgebra.2015.02.034

The connectedness of hessenberg varieties

Martha Precup^*

^*Corresponding author for this work

Mathematics

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

7 Scopus citations

Abstract

In this paper we consider certain closed subvarieties of the flag variety, known as Hessenberg varieties. These varieties arise in representation theory, algebraic geometry, and combinatorics. We give a connectedness criterion for semisimple Hessenberg varieties that generalizes a criterion given by Anderson and Tymoczko. It also generalizes results of Iveson in type A which prove that all Hessenberg varieties satisfying this criterion are connected. We then show that nilpotent Hessenberg varieties are rationally connected.

Original language	English (US)
Pages (from-to)	34-43
Number of pages	10
Journal	Journal of Algebra
Volume	437
DOIs	https://doi.org/10.1016/j.jalgebra.2015.02.034
State	Published - Sep 1 2015

Keywords

Affine paving
Hessenberg varieties
Rationally connected

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2015.02.034

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abstract = "In this paper we consider certain closed subvarieties of the flag variety, known as Hessenberg varieties. These varieties arise in representation theory, algebraic geometry, and combinatorics. We give a connectedness criterion for semisimple Hessenberg varieties that generalizes a criterion given by Anderson and Tymoczko. It also generalizes results of Iveson in type A which prove that all Hessenberg varieties satisfying this criterion are connected. We then show that nilpotent Hessenberg varieties are rationally connected.",

keywords = "Affine paving, Hessenberg varieties, Rationally connected",

author = "Martha Precup",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2015",

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AB - In this paper we consider certain closed subvarieties of the flag variety, known as Hessenberg varieties. These varieties arise in representation theory, algebraic geometry, and combinatorics. We give a connectedness criterion for semisimple Hessenberg varieties that generalizes a criterion given by Anderson and Tymoczko. It also generalizes results of Iveson in type A which prove that all Hessenberg varieties satisfying this criterion are connected. We then show that nilpotent Hessenberg varieties are rationally connected.

KW - Affine paving

KW - Hessenberg varieties

KW - Rationally connected

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SP - 34

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

The connectedness of hessenberg varieties

Abstract

Keywords

ASJC Scopus subject areas

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