{
  "abstract": "Let $T^p c_r$ be the $p$-osculating variety of the rational normal curve $c_r\\subset\\mathbb{P}S^r(\\mathbb{C}^2)$. We study its quadratic hull, the scheme defined by the quadratic equations vanishing on $T^p c_r$. For $r\\ge2p+3$, we prove that this scheme is a complete intersection of $\\binom{r-2p}{2}$ quadrics whenever \\[ p\\ge\\binom{r-2p-1}{2}. \\] When the inequality is strict, the hull is integral and strictly contains $T^p c_r$. On the boundary its support is reducible, except for $(p,r)=(1,5)$, where the hull equals the osculating variety. The proof is local at the highest weight point. Koornwinder's relation between Clebsch--Gordan coefficients and Hahn polynomials leads to a description of the tangent-cone equations in which each antidiagonal becomes an ordinary polynomial space of bounded degree. An incidence estimate then gives a normal integral tangent cone in the strict range, and the $SL_2$-action turns this local statement into global integrality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28499",
  "author_total": 1,
  "authors": [
    {
      "name": "César Massri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9mxcw0thp6pd4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28499",
  "fulltext_url": null,
  "id": "9mxcw0thp6pd4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28499",
  "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",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223125045",
  "pdf_url": "https://arxiv.org/pdf/2610.28499",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9mxcw0thp6pd4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28499",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28499"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quadratic hulls of osculating varieties of rational normal curves",
  "title_text": "Quadratic hulls of osculating varieties of rational normal curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/9mxcw0thp6pd4",
  "venue": "arXiv",
  "versions": []
}