The local-orbifold correspondence for simple normal crossings pairs

Abstract

For $X$ a smooth projective variety and $D=D_1+\ldots+D_n$ a simple normal crossings divisor, we establish a precise cycle-level correspondence between the genus zero local Gromov-Witten theory of the bundle $\oplus_{i=1}^n \mathcal{O}_X(-D_i)$ and the maximal contact Gromov-Witten theory of the multi-root stack $X_{D,\vec{r}}$. The proof is an implementation of the rank reduction strategy. We use this point of view to clarify the relationship between logarithmic and orbifold invariants.