{
  "abstract": "Let $\\cX$ be a (projective, geometrically irreducible, non-singular) algebraic curve of genus $\\ge 2$ and positive $p$-rank $γ(\\cX)$, defined over an algebraically closed field $\\mathbb{K}$ of positive characteristic $p>0$. Contrary to what occurs for the genus, no function $h(γ)$ exists such that $|\\aut(\\cX)|\\le h(γ)$ whenever $γ=γ(\\cX)$. Thus, to have a bound on $|\\aut(\\cX)|$ only depending on $γ(\\cX)$, some restrictions on $\\cX$ and $\\aut(\\cX)$ are needed. In this context, the following theorem is proven. Let $Γ$ be a subgroup of $\\aut(\\cX)$. Assume that there is a point $P\\in \\cX$ such that the quotient curve $\\cX/S_P$ is rational, where $S_P$ denotes the Sylow p-subgroup of the stabilizer $Γ_P$ of $P$ in $Γ$. Then the following $p$-rank analog of the Riemann-Hurwitz bound \\begin{equation*} |Γ|\\le 24 \\left(\\frac{p}{p-1}\\right)^4 γ(\\cX)^4 \\end{equation*} holds, unless a subgroup of index $\\le 2$ of $Γ$ fixes $P$. This bound is sharp up to a constant depending only on $p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.10065",
  "author_total": 3,
  "authors": [
    {
      "name": "Massimo Giulietti"
    },
    {
      "name": "Gábor Korchmáros"
    },
    {
      "name": "Marco Timpanella"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9bmh5k6gqsd80.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.10065",
  "fulltext_url": null,
  "id": "9bmh5k6gqsd80",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.10065",
  "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": "W7164172732",
  "pdf_url": "https://arxiv.org/pdf/2606.10065",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9bmh5k6gqsd80.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2606.10065",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.10065"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Large automorphism groups compared to the $p$-rank of algebraic curves in characteristic $p$",
  "title_text": "Large automorphism groups compared to the p-rank of algebraic curves in characteristic p",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9bmh5k6gqsd80",
  "venue": "arXiv",
  "versions": []
}