Splitting of Gromov-Witten Invariants with Toric Gluing Strata

Abstract

We prove a splitting formula that reconstructs the logarithmic Gromov- Witten invariants of simple normal crossing varieties from the punctured Gromov- Witten invariants of their irreducible components, under the assumption of the gluing strata being toric varieties. The formula is based on the punctured Gromov-Witten theory developed in arXiv:2009.07720.

arXiv comment44 pages. v2: Minor corrections throughout the text v3: Corrected minor mistakes. Restated Def 1.4 and added Remark 1.5

References in corpus (11)

• The tropicalization of the moduli space of curves
• Functorial tropicalization of logarithmic schemes: The case of constant coefficients
• Orbifold techniques in degeneration formulas
• Stable logarithmic maps to Deligne--Faltings pairs II
• Decomposition of degenerate Gromov-Witten invariants
• The moduli stack of $G$-bundles
• Chow rings of stacks of prestable curves I
• Punctured logarithmic maps
• The degeneration formula for stable log maps
• Tropical gluing formulae for Gromov-Witten invariants
• Three dimensional tropical correspondence formula

Cited by in corpus (2)

• The canonical wall structure and intrinsic mirror symmetry
• Towards the Doran-Harder-Thompson conjecture via the Gross-Siebert program