Cluster Structures and Subfans in Scattering Diagrams

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2020
• 1. Verfasser: Zhou, Yan
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2020
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/210597
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Cluster Structures and Subfans in Scattering Diagrams. Yan Zhou. SIGMA 16 (2020), 013, 35 pages

We give more precise statements of the Fock-Goncharov duality conjecture for cluster varieties parametrizing SL₂/PGL₂-local systems on the once-punctured torus. Then we prove these statements. Along the way, using distinct subfans in the scattering diagram, we produce an example of a cluster variety...