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# Communications in Analysis and Geometry

## Volume 24 (2016)

### Number 2

### Gromov–Witten theory of product stacks

Pages: 223 – 277

DOI: http://dx.doi.org/10.4310/CAG.2016.v24.n2.a1

#### Authors

#### Abstract

Let $\mathcal{X}_1$ and $\mathcal{X}_2$ be smooth proper Deligne–Mumford stacks with projective coarse moduli spaces. We prove a formula expressing 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.

Published 14 June 2016