{
  "abstract": "Given a family of genus $g$ curves $f:Ψ\\to S$ and a relative degree $d$ line bundle $L$ on $Ψ$ such that $f_*L$ is a vector bundle, the projectivization $\\mathbb{P}(f_*L)$ is stratified by relative de Jonquières loci, which parameterize sections of $L$ with prescribed vanishing orders. We give universal formulas for the classes of these loci in terms of the relative $O(1)$ on $\\mathbb{P}(f_*L)$ and tautological classes pulled back from the universal Picard stack $\\mathrm{Pic}_g^d$. When $f$ is the family of lines in $\\mathbb{P}^r$, we use the universal polynomials to compute $\\mathrm{GL}_{r+1}$-equivariant classes of loci of hypersurfaces and complete intersections admitting lines with prescribed contact orders.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30892",
  "author_total": 1,
  "authors": [
    {
      "name": "Smita Rajan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7xrng9jggfzr3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30892",
  "fulltext_url": null,
  "id": "7xrng9jggfzr3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30892",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.30892",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7xrng9jggfzr3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30892",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30892"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Universal Formulas for de Jonquières Loci and Equivariant Contact Problems",
  "title_text": "Universal Formulas for de Jonquières Loci and Equivariant Contact Problems",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/7xrng9jggfzr3",
  "venue": "arXiv",
  "versions": []
}