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arXiv · 2610.28114

Divisors on regular Hessenberg varieties for h=(2,3,4,...,n,n) associated to lower subsets

Hiraku Abe·Haozhi Zeng
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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.

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Hiraku Abe, Haozhi Zeng. 2026-10-20. Divisors on regular Hessenberg varieties for h=(2,3,4,...,n,n) associated to lower subsets. https://arxiv.org/abs/2610.28114

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