论文标题
$ q $-painlevé方程在群泊托彭森品种中通过曲折的几何形状
$q$-Painlevé equations on cluster Poisson varieties via toric geometry
论文作者
论文摘要
我们通过使用与$ q $-painlevé方程相关的有理表面的复合模型来提供$ q $-painlevé方程的几何框架与群集Poisson品种之间的关系。我们通过与种子相关的对称双线性形式的负半定义性介绍了$ q $painlevé类型的种子概念，并对这些种子的突变等效类别进行分类。该分类与Sakai给出的$ Q $-Painlevé方程式的分类相吻合。我们将$ Q $-Painlevé系统视为与$ Q $-Painlevé类型的种子相关的集群Poisson品种的自动形态。
We provide a relation between the geometric framework for $q$-Painlevé equations and cluster Poisson varieties by using toric models of rational surfaces associated with $q$-Painlevé equations. We introduce the notion of seeds of $q$-Painlevé type by the negative semi-definiteness of symmetric bilinear forms associated with seeds, and classify the mutation equivalence classes of these seeds. This classification coincides with the classification of $q$-Painlevé equations given by Sakai. We realize $q$-Painlevé systems as automorphisms on cluster Poisson varieties associated with seeds of $q$-Painlevé type.
