Quivers, curves, and the tropical vertex
By Mark Gross, R. Pandharipande. 2009
61 citations recorded by the source corpus.
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 previous conjectures by Gross-Siebert and Kontsevich). Where possible, we present both the quiver and Gromov-Witten perspectives.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2a3742c556c1bc23f4ea61c2c12f8117f8af308e
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In Discrete Mathematics and Combinatorics
- P. Hacking
- S. Keel
- M. Kontsevich
- Mark Gross
- Bernd S Siebert
- Jürgen Hausen
- Gonçalo Tabuada
- Ben Davison
In Geometry and Topology
Citations in the corpus
- Framed BPS states (2010, unknown): “The spectrum of populated charges in that region has been computed [37], and the result makes it clear what the difficulty is: the phases of Zγ for Ω(γ) 6= 0 are dense in that region, so that it is not really possible to speak about chambers.”
- Canonical bases for cluster algebras (2014, methodology): “ 1 ,1+A c 2),(e⊥ 2 ,1+A −b 1 )}. For most choices of band c, this is a very complicated scattering diagram. A very similar scattering diagram, with functions (1+A2)b and (1+A1)c, has been analyzed in [GP10], but it is easy to translate this latter diagram to the one considered here by replacing A1 b”