On Quasimodularity of Some Equivariant Intersection Numbers on the Hilbert Schemes

TL;DR

This paper demonstrates that specific equivariant intersection numbers on Hilbert schemes can be computed via the Bloch-Okounkov formula, linking them to Gromov-Witten invariants of elliptic curves and operator formalism in Fock space.

Contribution

It reveals a quasimodular structure of equivariant intersection numbers on Hilbert schemes and connects them to elliptic Gromov-Witten invariants using operator formalism.

Findings

Equivariant intersection numbers relate to Gromov-Witten invariants.

Use of Bloch-Okounkov formula to compute intersection numbers.

Identification of quasimodularity in the context of Hilbert schemes.

Abstract

We observe that certain equivariant intersection numbers of Chern characters of tautological sheaves on Hilbert schemes for suitable circle actions can be computed using the Bloch-Okounkov formula, hence they are related to Gromov-Witten invariants of elliptic curves and its operator formalism in terms of operators on the Fock space.