{
  "abstract": "We show the existence of a quartic form of strength $3$ in the closure of the strength at most $2$ locus, answering a question of Ballico--Bik--Oneto--Ventura in the negative. In the analogous setting of partition rank as introduced by Naslund, we further show that the locus of tensors of partition rank at most $2$ is closed, but the locus of tensors of partition rank at most $3$ is not. Together with a suspension lemma, this answers for all $r$ whether the locus of forms/tensors of strength/partition rank at most $r$ is Zariski-closed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28792",
  "author_total": 2,
  "authors": [
    {
      "name": "Benjamin Baily"
    },
    {
      "name": "Alessandro Danelon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vey3vkjfdt3n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28792",
  "fulltext_url": null,
  "id": "2vey3vkjfdt3n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28792",
  "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.AC"
    ],
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      "arxiv",
      "math.AG"
    ],
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      "arxiv",
      "math.RA"
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      "openalex",
      "2605|Tensor decomposition and applications"
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  "openalex": "W7223213800",
  "pdf_url": "https://arxiv.org/pdf/2610.28792",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vey3vkjfdt3n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.28792",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28792"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Closedness of bounded strength and partition rank loci",
  "title_text": "Closedness of bounded strength and partition rank loci",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/2vey3vkjfdt3n",
  "venue": "arXiv",
  "versions": []
}