{
  "abstract": "For an $n$-fold geometrically cyclic branched covering $Y$ of a smooth, projective scheme $X$ branched at a smooth closed subscheme $Z\\subset X$ with $n \\in k^\\times$, we compute the quadratic Euler characteristic of $Y$ in terms of certain Euler classes on $X$ and $Z$ using the quadratic Riemann-Hurwitz formula of Levine. When $n$ is odd, we relate the quadratic Euler characteristic of $Y$ to the quadratic Euler characteristics of $X$ and $Z$, obtaining similar formulae to the situation in topology. As an application, we compute the quadratic Euler characteristic of geometrically cyclic branched double coverings of $\\mathbb{P}^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.13425",
  "author_total": 1,
  "authors": [
    {
      "name": "Louisa F. Bröring"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3dbw9nmf77ht.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.13425",
  "fulltext_url": null,
  "id": "e3dbw9nmf77ht",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.13425",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7161167261",
  "pdf_url": "https://arxiv.org/pdf/2605.13425",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3dbw9nmf77ht.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2605.13425",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.13425"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quadratic Euler Characteristic of Geometrically Cyclic Branched Coverings",
  "title_text": "Quadratic Euler Characteristic of Geometrically Cyclic Branched Coverings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/e3dbw9nmf77ht",
  "venue": "arXiv",
  "versions": []
}