{
  "abstract": "The $b$-invariant of a normal graded ring was defined recently by Okuma, Watanabe, and Yoshida. We study this for invariant rings of finite groups, proving that it is nonpositive in the case of abelian groups, but not necessarily otherwise; more generally, we give a description of the anticanonical module for invariant rings of finite groups. Turning to infinite groups, we record the anticanonical module and the $b$-invariant for families of determinantal rings. We also construct standard-graded Cohen-Macaulay rings of characteristic zero, with isolated singularities and negative $b$-invariant, that are not of strongly $F$-regular type, thereby disproving a conjecture of Okuma-Watanabe-Yoshida.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32003",
  "author_total": 3,
  "authors": [
    {
      "name": "Aryaman Maithani"
    },
    {
      "name": "Anurag K. Singh"
    },
    {
      "name": "Kei-ichi Watanabe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3sjgbmc4ygaz1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32003",
  "fulltext_url": null,
  "id": "3sjgbmc4ygaz1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32003",
  "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": "W7214775164",
  "pdf_url": "https://arxiv.org/pdf/2609.32003",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3sjgbmc4ygaz1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2609.32003",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32003"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the $b$-invariant of a normal graded ring",
  "title_text": "On the b-invariant of a normal graded ring",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/3sjgbmc4ygaz1",
  "venue": "arXiv",
  "versions": []
}