Decomposition of degenerate Gromov-Witten invariants

2017/09/28 by Dan Abramovich, Qile Chen, Abramovich, Dan +5 · 5 citations
Mathematics · Chemistry · Biochemistry, Genetics and Molecular Biology · #Algebraic Geometry and Number Theory #Synthesis and pharmacology of benzodiazepine derivatives #Biological Activity of Diterpenoids and Biflavonoids

paper · pdf · doi:10.48550/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 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 X_b0 is a normal crossings union of two divisors. We exhibit our formulas in explicit examples.

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