The tropical vertex
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- 1 June 2010
- journal article
- Published by Duke University Press in Duke Mathematical Journal
- Vol. 153 (2) , 297-362
Abstract
Elements of the tropical vertex group are formal families of symplectomorphisms of the 2-dimensional algebraic torus. We prove that ordered product factorizations in the tropical vertex group are equivalent to calculations of certain genus zero 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 theoryKeywords
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