On singularity and normality of regular nilpotent Hessenberg varieties

2022/12/28 by Abe, Hiraku, Insko, Erik · 1 citation
#14M15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.13817

Abstract

Regular nilpotent Hessenberg varieties form an important family of subvarieties of the flag variety, which are often singular and sometimes not normal varieties. Like Schubert varieties, they contain distinguished points called permutation flags. In this paper, we give a combinatorial characterization for a permutation flag of a regular nilpotent Hessenberg variety to be a singular point. We also apply this result to characterize regular nilpotent Hessenberg varieties which are normal algebraic varieties.

Cited by

• Coordinate rings of regular semisimple Hessenberg varieties and cohomology rings of regular nilpotent Hessenberg varieties

Related

• Hessenberg varieties are not pure dimensional
• Regular Hessenberg varieties for the minimal indecomposable Hessenberg space
• Hessenberg varieties of codimension one in the flag variety
• Towards combinatorial characterization of the smoothness of Hessenberg Schubert varieties
• Linear conditions imposed on flag varieties