The tropical vertex
Algebraic Geometry
2019-12-19 v2 Symplectic Geometry
Abstract
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.
Cite
@article{arxiv.0902.0779,
title = {The tropical vertex},
author = {Mark Gross and Rahul Pandharipande and Bernd Siebert},
journal= {arXiv preprint arXiv:0902.0779},
year = {2019}
}
Comments
57 pages, 1 figure; some typoes corrected and additional references given. Example 1.11 added