Gromov-Witten theory of product stacks

TL;DR

This paper establishes a formula relating the orbifold Gromov-Witten invariants of a product stack to those of its factors, enabling decomposition results for Gromov-Witten theory of trivial gerbes.

Contribution

It introduces a new formula for orbifold Gromov-Witten invariants of product stacks, connecting them to invariants of individual factors, advancing the understanding of Gromov-Witten theory for stacks.

Findings

Derived a formula for orbifold Gromov-Witten invariants of product stacks.

Proved a decomposition result for Gromov-Witten theory of trivial gerbes.

Enhanced computational tools for Gromov-Witten invariants of stacks.

Abstract

Let $\mathcal{X}_1$ and $\mathcal{X}_2$ be smooth proper Deligne-Mumford stacks with projective coarse moduli spaces. We prove a formula for orbifold Gromov-Witten invariants of the product stack $\mathcal{X}_1\times \mathcal{X}_2$ in terms of Gromov-Witten invariants of the factors $\mathcal{X}_1$ and $\mathcal{X}_2$. As an application, we deduce a decomposition result for Gromov-Witten theory of trivial gerbes.