The local-orbifold correspondence for simple normal crossings pairs

Abstract

For $X$ a smooth projective variety and $D=D_1+\dots +D_n$ 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.

arXiv comment14 pages. Comments welcome! Final version to appear in Journal of the Institute of Mathematics of Jussieu

References in corpus (10)

• Computing Genus-Zero Twisted Gromov-Witten Invariants
• Enumerative geometry of Calabi-Yau 4-folds
• The tropical vertex
• Orbifold techniques in degeneration formulas
• Local Gromov-Witten Invariants are Log Invariants
• Gromov-Witten theory with maximal contacts
• Higher genus relative and orbifold Gromov-Witten invariants
• Virtual push-forwards
• Relative quasimaps and mirror formulae
• A Gromov-Witten theory for simple normal-crossing pairs without log geometry

Cited by in corpus (4)

• Gromov-Witten theory with maximal contacts
• Stable maps to Looijenga pairs: orbifold examples
• The local/logarithmic correspondence and the degeneration formula for quasimaps
• The log-open correspondence for two-component Looijenga pairs