簇代数与散射图表，第三部分：簇散射图表
组合数学
2023-02-23 v6 数学物理
交换代数
math.MP
摘要
本文对 Gross、Hacking、Keel 和 Kontsevich 引入并研究的簇散射图表的若干基本性质给出了自包含阐述。特别地，给出了簇散射图表的构造、突变不变性以及 theta 函数正性的详细证明。全文强调了二重对数元与五角关系在簇散射图表中的基础作用。
引用
@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}
}
备注
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