Connected Gromov-Witten invariants of [Sym^n(A_r)]

TL;DR

This paper develops formulas for connected Gromov-Witten invariants of symmetric product stacks [Sym^n(A_r)] and uncovers a link to the relative Gromov-Witten theory of A_r x P^1, with explicit results for small n.

Contribution

It provides closed-form expressions for equivariant invariants with two insertions and establishes a correspondence with relative Gromov-Witten theory, advancing understanding of these invariants.

Findings

Derived closed-form formulas for all equivariant invariants with two insertions.

Established a natural correspondence with the relative Gromov-Witten theory of A_r x P^1.

Determined 3-point Gromov-Witten invariants for [Sym^n(A_1)] when n ≤ 3.

Abstract

We explore the theory of connected Gromov-Witten invariants of the symmetric product stack [Sym^n(A_r)]. We derive closed-form expressions for all equivariant invariants with two insertions and reveal a natural correspondence between the theory and the relative Gromov-Witten theory of the threefold A_r x P^1. When n is less than or equal to 3, we determine 3-point (usual) Gromov-Witten invariants of [Sym^n(A_1)].