图构型模型之间的一个同构
An isomorphism between models of graphic arrangements
AI总结：
本文研究图定义的环面构型与超平面构型精彩模型之间的同构关系，证明在适当选择构建集时，由图 Γ 定义的环面构型模型与由 Γ 的锥定义的超平面构型模型同构。
摘要：
本文在环面构型相关的精彩模型理论与超平面构型相关的精彩模型理论之间架起了一座桥梁。在之前的工作中，同一批作者注意到类型 $A_{n-1}$ 的环面构型的模型与类型 $A_{n}$ 的超平面构型的模型是同构的；自然要问，在其他构型族之间是否存在类似的同构。本文的目的是研究一个这样的族，即由图定义的构型族。主要结果表明，在选择了合适的构建集的前提下，由图 $Γ$ 定义的环面构型的模型与由 $Γ$ 的锥定义的超平面构型的模型之间确实存在一个同构。
英文摘要：
This paper presents a bridge between the theories of wonderful models associated with toric arrangements and wonderful models associated with hyperplane arrangements. In a previous work, the same authors noticed that the model of the toric arrangement of type $A_{n-1}$ is isomorphic to the one of the hyperplane arrangement of type $A_{n}$; it is natural to ask if there exist similar isomorphisms between other families of arrangements. The aim of this paper is to study one such family, namely the family of arrangements defined by graphs. The main result states that there is indeed an isomorphism between the model of a toric arrangement defined by a graph $Γ$ and the model of a hyperplane arrangement defined by the cone of $Γ$, provided that a suitable building set is chosen.
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