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PreprintCC BY 4.0arXiv

Quasi-modularity of q-traces and integrals over Hilbert schemes

  • Killian Hong-Minh
  • Sergey Mozgovoy
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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.

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Cite

BibTeXRIS
BibTeX
@misc{hongminh2026quasimodularity,
  title = {{Quasi-modularity of $q$-traces and integrals over Hilbert schemes}},
  author = {Killian Hong-Minh and Sergey Mozgovoy},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02049},
  eprint = {2610.02049},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02049},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quasi-modularity of q-traces and integrals over Hilbert schemes
AU  - Killian Hong-Minh
AU  - Sergey Mozgovoy
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02049
UR  - https://arxiv.org/abs/2610.02049
AB  - 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.
ER  -