{
  "abstract": "We prove a necessary condition conjecture ([27, Conjecture B]) for the maximal singularity of the Hilbert scheme of points in 3D for a large class of degrees, which in particular implies the 1978 Briançon-Iarrobino Conjecture for a tetrahedral degree, and vastly generalises the result in [19]. The novelty lies in introducing a new upper bound on the dimensions of the tangent spaces of the claimed non-maximally singular ideals, constructing canonical ideals that satisfy the claimed maximal singularity condition, providing a lower bound on the dimension of their tangent spaces, and finally comparing the two cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04054",
  "author_total": 2,
  "authors": [
    {
      "name": "Fatemeh Rezaee"
    },
    {
      "name": "Parsa Saberi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7avbyc0grr23w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04054",
  "fulltext_url": null,
  "id": "7avbyc0grr23w",
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  "landing_url": "https://arxiv.org/abs/2609.04054",
  "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.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CO"
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      "arxiv",
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      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  ],
  "openalex": "W7208743455",
  "pdf_url": "https://arxiv.org/pdf/2609.04054",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7avbyc0grr23w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.04054",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04054"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An obstruction to the maximal singularity of the Hilbert scheme of points on threefolds",
  "title_text": "An obstruction to the maximal singularity of the Hilbert scheme of points on threefolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/7avbyc0grr23w",
  "venue": "arXiv",
  "versions": []
}