{
  "abstract": "We study the behavior of Castelnuovo--Mumford regularity under integral closure. We prove a general cohomological criterion for the inequality $\\operatorname{reg}(\\overline J)\\leq \\operatorname{reg(J)}$, and in particular obtain it for every homogeneous ideal in a polynomial ring in at most three variables. The proof uses a high-degree comparison between $\\overline J$ and its saturation. We also give a saturated monomial counterexample in four variables, showing that the three-variable result is sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.13879",
  "author_total": 1,
  "authors": [
    {
      "name": "Soumyadeep Misra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cvgz828d6t45z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.13879",
  "fulltext_url": null,
  "id": "cvgz828d6t45z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.13879",
  "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"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7161280106",
  "pdf_url": "https://arxiv.org/pdf/2605.13879",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cvgz828d6t45z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2605.13879",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.13879"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Regularity under Integral Closure: A General Criterion and a Sharp Counterexample",
  "title_text": "Regularity under Integral Closure: A General Criterion and a Sharp Counterexample",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/cvgz828d6t45z",
  "venue": "arXiv",
  "versions": []
}