From GW invariants of symmetric product stacks to relative invariants of threefolds

Abstract

In this note, we relate the equivariant GW invariants of the symmetric product stacks of any nonsingular toric surface $X$ in genus zero to the equivariant relative GW invariants of the threefold $X \times \mathbb{P}^1$ in all genera. We give an example for which an equivalence between these two theories exists.