{
  "abstract": "For a line arrangement $\\mathcal{A} \\colon f=0$ in $\\mathbb{P}^2$, let $ν(\\mathcal{A})$ be the maximal dimension of a graded piece of the Jacobian module of $f$. We study the conjecture that $ν(\\mathcal{A})$ depends only on the intersection lattice of $\\mathcal{A}$. It is known that $\\mathcal{A}$ is free if and only if $ν(\\mathcal{A})=0$, 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 $5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33584",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexandru Dimca"
    },
    {
      "name": "Piotr Pokora"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ftdd03kh8ps05.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33584",
  "fulltext_url": null,
  "id": "ftdd03kh8ps05",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33584",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7214709045",
  "pdf_url": "https://arxiv.org/pdf/2609.33584",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ftdd03kh8ps05.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2609.33584",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33584"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A generalized Terao Conjecture for line arrangements",
  "title_text": "A generalized Terao Conjecture for line arrangements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/ftdd03kh8ps05",
  "venue": "arXiv",
  "versions": []
}