{
  "abstract": "Let \\( \\mathcal{S}_{g,n} \\subset \\mathcal{M}_g \\) be the locus of curves of genus \\( g \\geq 2 \\) admitting a model \\( y^n = h(x) \\) with \\( h \\) separable; such curves $C$ have a cyclic group \\( C_n \\leq \\operatorname{Aut}(C) \\) of order \\( n \\) with \\( C/C_n \\cong \\mathbb{P}^1 \\). % We give an algorithm which, given an absolutely irreducible plane model \\( F(x,y) = 0 \\) of a curve \\( C \\) over a field \\( k_0 \\) of characteristic zero, decides for which \\( n \\) the curve lies in \\( \\mathcal{S}_{g,n} \\) and returns a model \\( y^n = h(x) \\) together with the birational transformation to it.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00672",
  "author_total": 1,
  "authors": [
    {
      "name": "T. Shaska"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eh00b22wxb4mv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00672",
  "fulltext_url": null,
  "id": "eh00b22wxb4mv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00672",
  "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",
      "cs.SC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7206179530",
  "pdf_url": "https://arxiv.org/pdf/2609.00672",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eh00b22wxb4mv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00672",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00672"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Deciding superellipticity and computing the Weierstrass normal form",
  "title_text": "Deciding superellipticity and computing the Weierstrass normal form",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/eh00b22wxb4mv",
  "venue": "arXiv",
  "versions": []
}