{
  "abstract": "We study quasi-modularity of normalized $q$-traces on bosonic Fock spaces associated with finite-dimensional quadratic spaces and superspaces. For a natural class of operators obtained from free-boson fields and their descendants, we prove that their normalized $q$-traces are quasi-modular, with weight bounded by the sum of the weights of the insertions. As applications, we prove Qin's quasi-modularity conjecture for tautological integrals on Hilbert schemes of points of a surface with numerically trivial canonical class, obtain quasi-modularity of arbitrary zero-mode correlation functions in the Heisenberg vertex operator algebra, and give a new proof of the Bloch--Okounkov quasi-modularity theorem as a rank-one specialization of our general result.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02049",
  "author_total": 2,
  "authors": [
    {
      "name": "Killian Hong-Minh"
    },
    {
      "name": "Sergey Mozgovoy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8sb5fd7wbr011.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02049",
  "fulltext_url": null,
  "id": "8sb5fd7wbr011",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02049",
  "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.RT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7216511850",
  "pdf_url": "https://arxiv.org/pdf/2610.02049",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8sb5fd7wbr011.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.02049",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02049"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quasi-modularity of $q$-traces and integrals over Hilbert schemes",
  "title_text": "Quasi-modularity of q-traces and integrals over Hilbert schemes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/8sb5fd7wbr011",
  "venue": "arXiv",
  "versions": []
}