The tropical vertex

Details The tropical vertex The tropical vertex

2009-02-04

arxiv.org/abs/0902.0779v2

Mathematics

Algebraic Geometry

57 pages, 1 figure; some typoes corrected and additional references given. Example 1.11 added

Scientific paper

Elements of the tropical vertex group, introduced by Kontsevich and Soibelman, are formal families of symplectomorphisms of the 2-dimensional algebraic torus. We prove ordered product factorizations in the tropical vertex group are equivalent to calculations of certain genus 0 relative Gromov-Witten invariants of toric surfaces. The relative invariants which arise have full tangency to a toric divisor at a single unspecified point. The method uses scattering diagrams, tropical curve counts, degeneration formulas, and exact multiple cover calculations in orbifold Gromov-Witten theory.

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