Decomposition of degenerate Gromov-Witten invariants
arXiv:1709.09864
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_0 \in 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 b_0 in terms of rigid tropical curves. 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.
63 pages, major revision of v2: streamlined exposition with the core results rewritten with simplified and cleaner proofs (now in §2.4-2.6 and §3). To appear in Compositio Math. Accepted version
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