{
  "abstract": "We prove that, for every fixed $d\\geq 2$ and $\\varepsilon>0$, the $\\mathbb{F}_q$-points of a geometrically irreducible reflexive plane curve of degree $d$ over $\\mathbb{F}_q$ can be covered by at most $\\left(\\frac{1}{d}+\\varepsilon\\right)q$ many $\\mathbb{F}_q$-lines, provided that $q$ is sufficiently large. The same conclusion holds for $\\mathbb{F}_q$-irreducible curves that are not geometrically irreducible, since they have only $O(d^2)$ $\\mathbb{F}_q$-points. In particular, for sufficiently large $q$, the bound applies to every $\\mathbb{F}_q$-irreducible plane curve of degree $d$ when $\\operatorname{char}(\\mathbb{F}_q)>d$. Our bound is asymptotically sharp. The proof combines Entin's Chebotarev density theorem for varieties over finite fields with the Pippenger--Spencer theorem on covers of nearly regular hypergraphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13042",
  "author_total": 5,
  "authors": [
    {
      "name": "Shamil Asgarli"
    },
    {
      "name": "Sarthak Dassarma"
    },
    {
      "name": "Dragos Ghioca"
    },
    {
      "name": "Simon MacLean"
    },
    {
      "name": "Evan Stokdyk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fc6ag78tdbjqm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13042",
  "fulltext_url": null,
  "id": "fc6ag78tdbjqm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13042",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221525549",
  "pdf_url": "https://arxiv.org/pdf/2610.13042",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fc6ag78tdbjqm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13042",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13042"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Covering plane curves over finite fields with lines",
  "title_text": "Covering plane curves over finite fields with lines",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/fc6ag78tdbjqm",
  "venue": "arXiv",
  "versions": []
}