{
  "abstract": "We give counterexamples to the conjecture of Dais-Henk-Ziegler on projective crepant resolutions of complete-intersection quotient singularities. For finite $G\\subset\\operatorname{SL}_4(\\mathbb{Z})$, we determine whether $\\mathbb{C}^4/G$ admits a projective crepant resolution, with the representations considered up to conjugacy in $\\operatorname{SL}_4(\\mathbb{C})$. Ten explicit criteria decide all cases. The examples also show that the Molien series and the age polynomial do not determine existence. We also discuss questions of Ito-Reid on maximal cyclic subgroups and the generation of cohomology in degree two.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16962",
  "author_total": 2,
  "authors": [
    {
      "name": "Dominik Burek"
    },
    {
      "name": "Sławomir Cynk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6x80pn128tyy4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16962",
  "fulltext_url": null,
  "id": "6x80pn128tyy4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16962",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221760625",
  "pdf_url": "https://arxiv.org/pdf/2610.16962",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6x80pn128tyy4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:16Z",
      "native_id": "2610.16962",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16962"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Crepant resolutions of four-dimensional finite quotients",
  "title_text": "Crepant resolutions of four-dimensional finite quotients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:16Z",
  "url": "https://research.draconitic.com/paper/6x80pn128tyy4",
  "venue": "arXiv",
  "versions": []
}