Cluster Structures and Subfans in Scattering Diagrams

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• ISSN: 1815-0659
• Main Author: Zhou, Yan
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210597
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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...