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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,…,n,n), we construct Cartier divisors DA associated to lower subsets ∅subsetneq Asubsetneq[n]. We show that their first Chern classes satisfy the quadratic relations suggested by the combination of the works of Bbrevealibanu-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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Cite

BibTeXRIS
BibTeX
@misc{abe2026divisors,
  title = {{Divisors on regular Hessenberg varieties for h=(2,3,4,...,n,n) associated to lower subsets}},
  author = {Hiraku Abe and Haozhi Zeng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28114},
  eprint = {2610.28114},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28114},
}
RIS
TY  - UNPB
TI  - Divisors on regular Hessenberg varieties for h=(2,3,4,...,n,n) associated to lower subsets
AU  - Hiraku Abe
AU  - Haozhi Zeng
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28114
UR  - https://arxiv.org/abs/2610.28114
AB  - For a regular Hessenberg variety associated to the Hessenberg function h=(2,3,4,…,n,n), we construct Cartier divisors D_A associated to lower subsets ∅subsetneq Asubsetneq[n]. We show that their first Chern classes satisfy the quadratic relations suggested by the combination of the works of Bbrevealibanu-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.
ER  -