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THE LOCAL-ORBIFOLD CORRESPONDENCE FOR SIMPLE NORMAL CROSSING PAIRS
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 22 / Issue 5 / September 2023
- Published online by Cambridge University Press:
- 25 March 2022, pp. 2515-2531
- Print publication:
- September 2023
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- Article
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For X a smooth projective variety and
$D=D_1+\dotsb +D_n$ a simple normal crossing divisor, we establish a precise cycle-level correspondence between the genus 
$0$ 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 multiroot 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.
