Decomposition of degenerate Gromov-Witten invariants
Abstract
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 curves. 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.
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