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 b(0) is an element of B yields a family M(X/B, beta). B of moduli stacks of stable logarithmic maps. We give a virtual decomposition of the fibre of this family over b(0) 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 Xb(0) is a normal crossings union of two divisors. We exhibit our formulas in explicit examples.