Cluster Algebras and Scattering Diagrams, Part III. Cluster Scattering Diagrams
Abstract
This is a self-contained exposition of several fundamental properties of cluster scattering diagrams introduced and studied by Gross, Hacking, Keel, and Kontsevich. In particular, detailed proofs are presented for the construction, the mutation invariance, and the positivity of theta functions of cluster scattering diagrams. Throughout the text we highlight the fundamental roles of the dilogarithm elements and the pentagon relation in cluster scattering diagrams.
Keywords
Cite
@article{arxiv.2111.00800,
title = {Cluster Algebras and Scattering Diagrams, Part III. Cluster Scattering Diagrams},
author = {Tomoki Nakanishi},
journal= {arXiv preprint arXiv:2111.00800},
year = {2023}
}
Comments
v1: 95 pp; v2: 106 pp, Sec. 5.4, 6.7 added; v3: 106 pp, Def 1.1 corrected; v4: 108 pp, proof of Lemma 4.6 corrected, index added; v5: 110 pp; v6: 110 pp. This is the final manuscript of Part III of the monograph "Cluster Algebras and Scattering Diagrams'', MSJ Mem. 41 (2023) by the author