{
  "abstract": "Let $Q$ be a Gorenstein local ring, let $I$ be a proper ideal of $Q$, and set $R=Q/I$. We investigate when finite injective dimension of the conormal module $I/I^2$ forces $I$ to be generated by a regular sequence. We prove this implication for every ideal in the linkage class of a complete intersection. When $Q$ is regular, we also establish it under several numerical conditions in terms of the number of generators of $I$ and the type of $R$. For normal domain quotients, we show that finite injective dimension of $I/I^2$ forces $(\\mathrm{ht}(I)+1)[ω_R]=0$ in $\\operatorname{Cl}(R)$, yielding the desired conclusion when the divisor class group is torsionfree. In the graded setting, we further prove the implication for all monomial ideals in polynomial rings. We also obtain a converse to Kunz's description of the first Koszul homology of an almost complete intersection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04031",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohsen Gheibi"
    },
    {
      "name": "Kaito Kimura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cv5aa6433hs9b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04031",
  "fulltext_url": null,
  "id": "cv5aa6433hs9b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04031",
  "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": "W7220668429",
  "pdf_url": "https://arxiv.org/pdf/2610.04031",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cv5aa6433hs9b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.04031",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04031"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On injective dimension of the conormal module",
  "title_text": "On injective dimension of the conormal module",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/cv5aa6433hs9b",
  "venue": "arXiv",
  "versions": []
}