Quivers, curves, and the tropical vertex

  title={Quivers, curves, and the tropical vertex},
  author={Mark Gross and Rahul Pandharipande},
  journal={arXiv: Algebraic Geometry},
Elements of the tropical vertex group are formal families of symplectomorphisms of the 2-dimensional algebraic torus. Commutators in the group are related to Euler characteristics of the moduli spaces of quiver representations and the Gromov-Witten theory of toric surfaces. After a short survey of the subject (based on lectures of Pandharipande at the 2009 Geometry summer school in Lisbon), we prove new results about the rays and symmetries of scattering diagrams of commutators (including… 

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