{
  "abstract": "In a previous paper ${\\bf [P1]}$, for every $n\\geq 2$, we studied the curvilinear web $\\boldsymbol{\\mathcal W}_{0,n+3}$ on the moduli space $\\boldsymbol{\\mathcal M}_{0,n+3}$, defined by the $n+3$ forgetful maps $ \\boldsymbol{\\mathcal M}_{0,n+3}\\rightarrow \\boldsymbol{\\mathcal M}_{0,n+2}$, with particular emphasis on its abelian relations. In particular, when $n$ is even, we conjectured an explicit formula for its Euler abelian relation. This relation is constructed à la Gelfand-MacPherson from an invariant differential form representing the appropriate power of the Euler class of the tautological bundle of the Grassmannian manifold $G_2^{\\mathrm{or}}(\\mathbf R^{n+3})$ of oriented $2$-planes in $\\mathbf R^{n+3}$. In this note, we obtain an explicit antisymmetrized formula for Euler's abelian relation for every even $n\\geq 2$, and prove that it coincides, up to the explicit factor $-(n+1)(n+2)/2$, with the formula conjectured in ${\\bf [P1]}$, which is therefore established for all even $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28956",
  "author_total": 1,
  "authors": [
    {
      "name": "Luc Pirio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0gwkjk6xs5qtk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28956",
  "fulltext_url": null,
  "id": "0gwkjk6xs5qtk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28956",
  "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.CV"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223230395",
  "pdf_url": "https://arxiv.org/pdf/2610.28956",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0gwkjk6xs5qtk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.28956",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28956"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On Euler's abelian relation of the web induced by the forgetful maps on the moduli space $\\boldsymbol{\\mathcal M_{0,n+3}}$: the case when $n$ is even",
  "title_text": "On Euler's abelian relation of the web induced by the forgetful maps on the moduli space ℳ_0,n+3: the case when n is even",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/0gwkjk6xs5qtk",
  "venue": "arXiv",
  "versions": []
}