{
  "abstract": "We prove the intersection product formulas of Gaffney and Gassler for polar multiplicities and Segre numbers over arbitrary Noetherian local rings. For equidimensional and universally catenary rings, we give a geometric refinement of the Principle of Specialization of Integral Dependence, in which the maximal dimension of the images of exceptional components mapping into the hypersurface determines a precise Segre number that strictly increases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06370",
  "author_total": 2,
  "authors": [
    {
      "name": "Yairon Cid-Ruiz"
    },
    {
      "name": "Steven Dale Cutkosky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/825eqhepxc7gs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06370",
  "fulltext_url": null,
  "id": "825eqhepxc7gs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06370",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06370",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/825eqhepxc7gs.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06370",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06370"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Intersection Product Formulas and Integral Dependence",
  "title_text": "Intersection Product Formulas and Integral Dependence",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/825eqhepxc7gs",
  "venue": "arXiv",
  "versions": []
}