{
  "abstract": "We introduce the categories $\\CM(X)$ and $\\SCM(X)$ of reflexive sheaves on a minimal partial resolution $f\\colon X \\to \\Spec R$ of a rational surface singularity $\\Spec R$. The main result of this paper establishes that $\\SCM(X)$ possesses a natural Frobenius structure, serving as a geometric counterpart to the algebraic Frobenius structure on special Cohen--Macaulay $R$-modules, introduced by Iyama--Wemyss and Iyama--Kalck--Wemyss--Yang. Utilizing this geometric framework, we establish an exact equivalence between $\\SCM(X)$ and the category of special Cohen--Macaulay $R$-modules equipped with a specific exact structure, which induces a triangle equivalence between their stable categories. Consequently, this provides a direct, geometric proof of the Iyama--Kalck--Wemyss--Yang equivalence and yields a Buchweitz-type equivalence $\\underline{\\SCM}(X) \\simeq D_{\\sg}(X)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30645",
  "author_total": 1,
  "authors": [
    {
      "name": "Hokuto Uehara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5qnmzba9n43d5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30645",
  "fulltext_url": null,
  "id": "5qnmzba9n43d5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30645",
  "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"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214642952",
  "pdf_url": "https://arxiv.org/pdf/2609.30645",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5qnmzba9n43d5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30645",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30645"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Special Cohen--Macaulay sheaves on partial resolutions of rational surfaces singularities",
  "title_text": "Special Cohen--Macaulay sheaves on partial resolutions of rational surfaces singularities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/5qnmzba9n43d5",
  "venue": "arXiv",
  "versions": []
}