Communications in Analysis and Geometry

Volume 24 (2016)

Number 2

Gromov–Witten theory of product stacks

Pages: 223 – 277



Elena Andreini (International School for Advanced Studies, Trieste, Italy)

Yunfeng Jiang (Department of Mathematics, University of Kansas, Lawrence Ks., U.S.A.)

Hsian-Hua Tseng (Department of Mathematics, Ohio State University, Columbus, Oh., U.S.A.)


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.

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