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arXiv · 2103.09299

The local-orbifold correspondence for simple normal crossings pairs

Luca Battistella·Navid Nabijou·Hsian-Hua Tseng·Fenglong You
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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.

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Luca Battistella, Navid Nabijou, Hsian-Hua Tseng, Fenglong You. 2021-03-16. The local-orbifold correspondence for simple normal crossings pairs. https://doi.org/10.1017/s1474748022000172

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