{
  "abstract": "We use an analogue of the Springer resolution to describe the $G$-module structure on the ring of regular functions on the universal cover $\\widetilde{\\mathcal{O}}$ of any nilpotent orbit for $G = SL_n$. Building on previous work on the extended Springer resolution, we construct a variety $\\widetilde{\\mathcal{M}}$ that is finite over the cotangent bundle of a partial flag variety $G/P$, and proper and birational over the affinization $\\mathcal{M}$ of $\\widetilde{\\mathcal{O}}$. We use techniques in birational geometry to show that $\\widetilde{\\mathcal{M}}$ has rational singularities, which provides the cohomology vanishing needed to describe the ring of functions on $\\widetilde{\\mathcal{O}}$ as an induced representation from a Levi subgroup of $G$. Our results also yield a description of the structure of $R(\\widetilde{\\mathcal{O}})$ as a graded $G$-module. We describe the minimal embedding of $\\mathcal{M}$, study the lifting of characters of the component group of $\\widetilde{\\mathcal{O}}$ to parabolics and Levi subgroups, and make a more general vanishing conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17272",
  "author_total": 3,
  "authors": [
    {
      "name": "William Graham"
    },
    {
      "name": "Scott Joseph Larson"
    },
    {
      "name": "Alberto San Miguel Malaney"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eptnq736qphpz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17272",
  "fulltext_url": null,
  "id": "eptnq736qphpz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17272",
  "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.AG"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7213433803",
  "pdf_url": "https://arxiv.org/pdf/2609.17272",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eptnq736qphpz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2609.17272",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17272"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Functions on Nilpotent Orbit Covers and Birational Geometry",
  "title_text": "Functions on Nilpotent Orbit Covers and Birational Geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/eptnq736qphpz",
  "venue": "arXiv",
  "versions": []
}