{
  "abstract": "Let $q$ be an odd prime power and let $X$ be a maximal curve of genus at least two over $\\F_{q^2}$. We prove that the automorphism group of $X$ acts transitively on its rational points if and only if $X$ is the Hermitian curve, or $q=5$ and $X$ is the unique $\\F_{25}$-maximal curve of genus $3$, namely the maximal Klein quartic. Together with the result of Giulietti and Korchmáros in characteristic two, this gives the classification for every prime power $q$. In particular, the Hermitian curve is the only maximal curve of genus at least two whose automorphism group is doubly transitive on its rational points.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17611",
  "author_total": 1,
  "authors": [
    {
      "name": "Saeed Tafazolian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/62syvmvy0wa6x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17611",
  "fulltext_url": null,
  "id": "62syvmvy0wa6x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17611",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213530094",
  "pdf_url": "https://arxiv.org/pdf/2609.17611",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/62syvmvy0wa6x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2609.17611",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17611"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Transitive automorphism groups of maximal curves",
  "title_text": "Transitive automorphism groups of maximal curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/62syvmvy0wa6x",
  "venue": "arXiv",
  "versions": []
}