An additive basis for the cohomology rings of regular nilpotent Hessenberg varieties

TL;DR

This paper constructs an additive basis for the cohomology rings of regular nilpotent Hessenberg varieties, extending Poincaré duals of smaller subvarieties, and proves their linear independence.

Contribution

It introduces a new additive basis for these cohomology rings by extending Poincaré duals, providing a deeper understanding of their structure.

Findings

Additive basis constructed for cohomology rings

Poincaré duals of smaller subvarieties are linearly independent

Extension method clarifies cohomology ring structure

Abstract

In this paper we construct an additive basis for the cohomology ring of a regular nilpotent Hessenberg variety which is obtained by extending all Poincar\'e duals of smaller regular nilpotent Hessenberg subvarieties. In particular, all of the Poincar\'e duals of smaller regular nilpotent Hessenberg subvarieties are linearly independent.