Year: 2026
Type: preprint
Abstract: For a regular Hessenberg variety associated to the Hessenberg function $h=(2,3,4,\ldots,n,n)$, we construct Cartier divisors $D_A$ associated to lower subsets $\emptyset\subsetneq A\subsetneq[n]$. We show that their first Chern classes satisfy the quadratic relations suggested by the combination of the works of B$\breve{\text{a}}$libanu-Crooks and Horiguchi-Masuda-Shareshian-Song. We also give a characterization of these divisors in terms of the centralizer action. It also follows that these divisors generate the (pseudo)effective cone of divisors on the Hessenberg variety.
Source: arXiv (Cornell University)
Authors: Abe, Hiraku, Zeng, Haozhi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223120515