{
  "annotation_id": "1a8cd05f-de04-47cb-932d-ce61d49bdd5a",
  "date_created": "2026-02-17T05:53:26.420000Z",
  "date_modified": "2026-02-17T05:53:26.420000Z",
  "file_hash": "f310cf335f0241a138aa8d03d50475c69a98298b4660c61f94165f562af1fa33",
  "private": false,
  "record": {
    "abstract": "This paper describes the vector bundle on the elliptic modular curve that is associated to a vertex operator algebra $V$ (VOA) or more generally a quasi-vertex operator algebra (QVOA), with a view towards future applications aimed at studying the characters of VOAs. We explain how the modes of sections of $V$ give rise naturally to $V$-valued quasi-modular forms. The space $Q(V)$ of $V$-valued quasi-modular forms is endowed with the structure of a doubled QVOA, and in particular the algebra $Q$ of quasi-modular forms is itself a doubled QVOA. $Q(V)$ also admits a natural derivative operator arising from the connection on the bundle defined by $V$ and the modular derivative, which we call the raising operator. We introduce an associated lowering operator $\\Lambda$ on $Q(V)$ having the property that the $V$-valued modular forms $M(V)\\subseteq Q(V)$ are the kernel of $\\Lambda$. This extends the classical theory of scalar-valued quasi-modular forms. We exhibit an explicit isomorphism of $M(V)$ with $M \\otimes V$. Finally, the coordinate invariance of vertex operators implies that $M(V)$ has a natural Hecke theory, and we use this isomorphism to fully describe the Hecke eigensystems: they are the same as the systems of eigenvalues that arise from scalar-valued quasi-modular forms.",
    "arxiv_id": "2601.10686",
    "authors": [
      "Daniel Barake",
      "Owen Chuchman",
      "Cameron Franc",
      "Geoffrey Mason",
      "Brett Nasserden"
    ],
    "categories": [
      "math.NT",
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Vertex operator algebra bundles on modular curves and their associated modular forms",
    "url": "https://arxiv.org/abs/2601.10686",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b6730657-306a-47d8-ada3-4125b3178b23",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}