Decomposition of degenerate Gromov–Witten invariants

We prove a decomposition formula of logarithmic Gromov–Witten invariants in a degeneration setting. A one-parameter log smooth family X B with singular fibre over b₀∈ B yields a family M(X/B,β ) B of moduli stacks of stable logarithmic maps. We give a virtual decomposition of the fibre of this family over b₀ in terms of rigid tropical maps to the tropicalization of $X/B$ . This generalizes one aspect of known results in the case that the fibre Xb₀ is a normal crossings union of two divisors. We exhibit our formulas in explicit examples.