{
  "abstract": "Let $X\\subset \\mathbb{O}^n$ be a nodal hypersurface of degree $d$ with an ordinary $m$-fold point. Let $δ_X$ be the largest value of $δ$ such that $X$ is contained in the closure of the Severi variety of degree $d$ hypersurface in $\\mathbb{P}^n$ with $δ$ nodes. After recalling how the semicontinuity of the spectrum yields an upper bound for $δ_X$, we produce various lower bounds for $δ_X$. These bounds are given by polynomials in $m$ of degree $n$, with different leading coefficients. This improves previous bounds given by Ciliberto-Galati.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18313",
  "author_total": 1,
  "authors": [
    {
      "name": "Remke Kloosterman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5z2y3e40b5hv7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18313",
  "fulltext_url": null,
  "id": "5z2y3e40b5hv7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18313",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213519160",
  "pdf_url": "https://arxiv.org/pdf/2609.18313",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5z2y3e40b5hv7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18313",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18313"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Nodal deformations of hypersurfaces with an ordinary $m$-fold point",
  "title_text": "Nodal deformations of hypersurfaces with an ordinary m-fold point",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/5z2y3e40b5hv7",
  "venue": "arXiv",
  "versions": []
}