{
  "abstract": "Let $F_n$ be the Fermat curve of degree $n$ over $\\mathbb Q$, and let $D_n=F_n/S_3$ be its quotient by coordinate permutations. We prove that $D_n$ has trivial geometric automorphism group for every $n\\ge 11$ with $\\gcd(n,6)=1$. Its Jacobian has complex multiplication. For $n=11$, this Jacobian is absolutely simple of dimension five. We construct an isogeny over $\\mathbb Q$ of degree $11^5$ from $\\operatorname{Jac}(D_{11})$ to the Jacobian of $y^{11}=x(1-x)^2$. For primes $p\\equiv 1\\pmod 3$, we also consider the metacyclic quotients $C_p$ of $F_p$ over $\\mathbb Q$. By a theorem of Carocca, Lange and Rodríguez, their Jacobians are absolutely simple and have complex multiplication. We prove that $C_p$ has trivial geometric automorphism group if and only if $p\\ge 19$. Write $p=r^2+rs+s^2$ with $r,s$ positive integers. The natural degree-three cover $Y_p\\to C_p$ satisfies $\\operatorname{gon}(Y_p)=r+s$, so $\\operatorname{gon}(C_p)\\ge \\lceil(r+s)/3\\rceil$. Since $g(C_p)=(p-1)/6$, both the genus and the gonality of $C_p$ tend to infinity with $p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08176",
  "author_total": 1,
  "authors": [
    {
      "name": "Saeed Tafazolian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1wtz50ys97g4v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08176",
  "fulltext_url": null,
  "id": "1wtz50ys97g4v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08176",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08176",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1wtz50ys97g4v.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08176",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08176"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Fermat quotients with CM Jacobians and trivial automorphism group",
  "title_text": "Fermat quotients with CM Jacobians and trivial automorphism group",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/1wtz50ys97g4v",
  "venue": "arXiv",
  "versions": []
}