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A generalized Terao Conjecture for line arrangements — arXiv:2609.33584

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.33584
License (as archived): CC0-1.0
Archived: 2026-10-07T23:29:26.380Z
SHA-256 of the archived text: 9bb45fa2ea7989e85a470c09e31d0e2e86732507af36e7cda6aedd847055d95c
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A generalized Terao Conjecture for line arrangements — arXiv:2609.33584 — arXiv (en), https://arxiv.org/abs/2609.33584 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ab77c19a5f92 (Metraipolis archive dc_ab77c19a5f92, sha256 9bb45fa2ea7989e85a470c09e31d0e2e86732507af36e7cda6aedd847055d95c)

BibTeX

@misc{dcab77c19a5f92,
  title = {A generalized Terao Conjecture for line arrangements — arXiv:2609.33584},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.33584},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ab77c19a5f92; sha256 9bb45fa2ea7989e85a470c09e31d0e2e86732507af36e7cda6aedd847055d95c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.33584. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

For a line arrangement $\mathcal{A} \colon f=0$ in $\mathbb{P}^2$, let $\nu(\mathcal{A})$ be the maximal dimension of a graded piece of the Jacobian module of $f$. We study the conjecture that $\nu(\mathcal{A})$ depends only on the intersection lattice of $\mathcal{A}$. It is known that $\mathcal{A}$ is free if and only if $\nu(\mathcal{A})=0$, and hence this conjecture is a strengthening of Terao's conjecture for line arrangements. We show that the conjecture holds for arrangements of at most $13$ lines, except possibly for arrangements of exactly $13$ lines whose intersection points have maximal multiplicity $5$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-29 in math.CO).
Categorie arXiv: Algebraic Geometry (math.AG) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.33584 — 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 2026-10-07T23:08:10.898Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).