Gromov-Witten theory of product 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.

38 pages