{
  "abstract": "Simple affine vertex operator algebras $L_k(\\mathfrak{g})$ at non-integral admissible levels $k$ are generally neither $C_2$-cofinite nor rational. Despite the absence of these standard finiteness conditions, we prove that the sheaf of coinvariants (and, dually, of conformal blocks) of ordinary modules in the category $\\mathcal{O}_k$ forms a vector bundle over the moduli space $\\overline{\\mathcal{M}}_{0,n}$ of stable $n$-pointed genus-zero curves. The proof relies on establishing the finite-dimensionality of genus-zero coinvariants, a vanishing theorem that isolates ordinary admissible modules at the boundary, and a smoothing theorem enabled by partial strong identity elements in the mode transition algebra. Consequently, admissible affine vertex operator algebras supply a rich class of non-rational, non-$C_2$-cofinite examples in which vector-bundle behavior is preserved for a well-behaved subcategory of modules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09154",
  "author_total": 2,
  "authors": [
    {
      "name": "Victor Alekseev"
    },
    {
      "name": "Jianqi Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2jrxmyb8resqy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09154",
  "fulltext_url": null,
  "id": "2jrxmyb8resqy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09154",
  "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"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7212055515",
  "pdf_url": "https://arxiv.org/pdf/2609.09154",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2jrxmyb8resqy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.09154",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09154"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Vector Bundles of Coinvariants for Admissible Affine Vertex Operator Algebras",
  "title_text": "Vector Bundles of Coinvariants for Admissible Affine Vertex Operator Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/2jrxmyb8resqy",
  "venue": "arXiv",
  "versions": []
}