{
  "abstract": "We consider the moduli stack $\\mathcal{H}_{g,d}$ parametrising maps $θ\\colon C\\to L$ of degree $d$ between complex curves of genera $g$ and $0$. We provide a splitting of the stable rational cohomology of $\\mathcal{H}_{g,d}$, for $g\\to\\infty$, in terms of degrees of intermediate covers, and identify each direct summand in terms of factorisation homology. For $2\\le d\\le 5$, we further interpret the stable rational cohomology in terms of configuration spaces with labels in partial abelian monoids; we show in particular the existence of stable odd-dimensional cohomology classes for $d=4,5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36884",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrea Bianchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/63q9966hbqchs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36884",
  "fulltext_url": null,
  "id": "63q9966hbqchs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36884",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7214990986",
  "pdf_url": "https://arxiv.org/pdf/2609.36884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/63q9966hbqchs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36884"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Stable rational cohomology splitting of moduli of branched covers of curves",
  "title_text": "Stable rational cohomology splitting of moduli of branched covers of curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/63q9966hbqchs",
  "venue": "arXiv",
  "versions": []
}