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Koszul Orlik--Solomon Algebras from Non-supersolvable Arrangements — arXiv:2609.03836

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.03836
License (as archived): CC0-1.0
Archived: 2026-10-17T02:33:26.742Z
SHA-256 of the archived text: 837b474d22979b93681ecea2a252c0d39111844edd49246c43f47025ff657b81
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How to cite

Koszul Orlik--Solomon Algebras from Non-supersolvable Arrangements — arXiv:2609.03836 — arXiv (en), https://arxiv.org/abs/2609.03836 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_216ab0f99bcb (Metraipolis archive dc_216ab0f99bcb, sha256 837b474d22979b93681ecea2a252c0d39111844edd49246c43f47025ff657b81)

BibTeX

@misc{dc216ab0f99bcb,
  title = {Koszul Orlik--Solomon Algebras from Non-supersolvable Arrangements — arXiv:2609.03836},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.03836},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_216ab0f99bcb; sha256 837b474d22979b93681ecea2a252c0d39111844edd49246c43f47025ff657b81},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.03836. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The cohomology ring of the complement of a complex hyperplane arrangement is given by its Orlik--Solomon algebra. It is known that the defining ideal of the Orlik--Solomon algebra has a quadratic Gröbner basis in the standard presentation if and only if the intersection lattice is supersolvable; such algebras are automatically Koszul. In 1997, Shelton and Yuzvinsky posed the question as to whether all Koszul Orlik--Solomon algebras arise from supersolvable arrangements. We answer this question negatively using three related constructions that produce non-supersolvable arrangements whose Orlik--Solomon algebras are Koszul. Moreover, these arrangements may be chosen to be irreducible, realizable over $\mathbb{Q}$, and of any rank $\geq 3$. Our constructions rely on a result of Falk and Proudfoot which we strengthen and generalize. In two of the three cases, we show non-supersolvability using a corrected form of a result of Ziegler regarding supersolvability of parallel connections. We also construct Koszul Orlik--Terao algebras coming from non-supersolvable arrangements.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-04 in math.CO).
Categorie arXiv: Combinatorics (math.CO) ; Commutative Algebra (math.AC); Algebraic Topology (math.AT); Rings and Algebras (math.RA).
Pagina del lavoro: https://arxiv.org/abs/2609.03836 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T02:09:21.188Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-04?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).