Cluster structures and subfans in scattering diagrams
Abstract
We give more precise statements of Fock-Goncharov duality conjecture for cluster varieties parametrizing -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 with two non-equivalent cluster structures. To overcome the technical difficulty of infinite non-cluster wall-crossing in the scattering diagram, we introduce quiver folding into the machinery of scattering diagrams and give a quotient construction of scattering diagrams.
Cite
@article{arxiv.1901.04166,
title = {Cluster structures and subfans in scattering diagrams},
author = {Yan Zhou},
journal= {arXiv preprint arXiv:1901.04166},
year = {2020}
}
Comments
Final version, a contribution to the Special Issue on Cluster Algebras of SIGMA. Many typos corrected. The proof of Theorem 2.20 cleaned up. The definition of a cluster structure of a log Calabi-Yau variety revised