发表机构
School of Mathematics, Trinity College Dublin; Hamilton Mathematics Institute（三一学院都柏林数学系; 哈密顿数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明玻色Fock空间上归一化$q$-迹的拟模性，并应用于证明Qin猜想、Heisenberg顶点算子代数零模关联函数拟模性及Bloch--Okounkov定理的新证明。
AI 中文摘要
我们研究了与有限维二次空间和超空间相关的玻色Fock空间上归一化$q$-迹的拟模性。对于由自由玻色场及其后代算子得到的一类自然算子类，我们证明了它们的归一化$q$-迹是拟模的，其权重由插入算子的权重之和界定。作为应用，我们证明了Qin关于数值典范类平凡曲面的Hilbert点概形上陈类重言积分的拟模性猜想，获得了Heisenberg顶点算子代数中任意零模关联函数的拟模性，并给出了Bloch--Okounkov拟模定理的一个新证明，该定理是我们一般结果的秩一特例。
英文摘要
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.
Comments35 pages
