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arXiv · 1709.09864

Decomposition of degenerate Gromov-Witten invariants

Dan Abramovich·Qile Chen·Mark Gross·Bernd Siebert
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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,\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 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.

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Dan Abramovich, Qile Chen, Mark Gross, Bernd Siebert. 2017-09-28. Decomposition of degenerate Gromov-Witten invariants. https://arxiv.org/abs/1709.09864

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