Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Hong-Minh, Killian, Mozgovoy, Sergey
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216511850