Decomposition of degenerate Gromov–Witten invariants. (19th October 2020) - Abramovich, Dan; Chen, Qile; Gross, Mark; Siebert, Bernd
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 b_0B 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 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 X_b_0 is a normal crossings union of two divisors. We exhibit our formulas in explicit examples.