The connectedness of hessenberg varieties

Martha Precup*

*Corresponding author for this work

Research output: Contribution to journalArticle

4 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 languageEnglish (US)
Pages (from-to)34-43
Number of pages10
JournalJournal of Algebra
Volume437
DOIs
StatePublished - Sep 1 2015

Keywords

  • Affine paving
  • Hessenberg varieties
  • Rationally connected

ASJC Scopus subject areas

  • Algebra and Number Theory

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