{
  "abstract": "Let ${\\mathcal L}$ be an arrangement of $d$ lines in the complex projective plane and let $Z={\\operatorname{Sing}}({\\mathcal L})$. A question of Pokora asks whether the multipoint Seshadri constant of ${\\mathcal O}_{\\mathbb{P}^2}(1)$ at $Z$ is always computed by a line of the arrangement containing the largest number of points of $Z$. We prove that the answer is affirmative for every arrangement of at most twelve lines. The proof uses a Bézout-type covering criterion, elementary restrictions on the intersection lattice, and a detailed analysis of the two extremal combinatorial types that can occur for twelve lines. One type is the Hesse arrangement; it is handled using a net of quartics through its twelve double points. The other type would yield a uniquely determined incidence structure on thirteen lines. We show that this incidence structure is not realizable over any field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03797",
  "author_total": 7,
  "authors": [
    {
      "name": "Marcin Dumnicki"
    },
    {
      "name": "Łucja Farnik"
    },
    {
      "name": "Krishna Hanumanthu"
    },
    {
      "name": "Brian Harbourne"
    },
    {
      "name": "Piotr Pokora"
    },
    {
      "name": "Joaquim Roé"
    },
    {
      "name": "Halszka Tutaj-Gasińska"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dfadqyhd1nkjd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03797",
  "fulltext_url": null,
  "id": "dfadqyhd1nkjd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03797",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03797",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dfadqyhd1nkjd.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03797",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03797"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Seshadri constants of singular loci of line arrangements with at most twelve lines",
  "title_text": "Seshadri constants of singular loci of line arrangements with at most twelve lines",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/dfadqyhd1nkjd",
  "venue": "arXiv",
  "versions": []
}