{
  "abstract": "We determine the multiplicative structure on the Tor algebras associated to the coordinate rings of general points in $\\mathbb{P}^3$ in terms of the number of points. We show that in codimension four, the Waring rank of a form determines the Tor algebra class of its apolar Artinian Gorenstein ring for a dense subset of the forms of fixed Waring rank and sufficiently large degree.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21060",
  "author_total": 1,
  "authors": [
    {
      "name": "Kara Fagerstrom"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dzkbk2qz3hxvz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21060",
  "fulltext_url": null,
  "id": "dzkbk2qz3hxvz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21060",
  "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"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7213935111",
  "pdf_url": "https://arxiv.org/pdf/2609.21060",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dzkbk2qz3hxvz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21060",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21060"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Classification of Tor algebras for rings from general points by Waring Rank",
  "title_text": "Classification of Tor algebras for rings from general points by Waring Rank",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/dzkbk2qz3hxvz",
  "venue": "arXiv",
  "versions": []
}