We study the connection between multimatroids and moduli spaces of rational curves with cyclic action. Multimatroids are generalizations of matroids and delta-matroids that naturally arise in topological graph theory. The perspective of moduli of curves provides a tropical framework for studying multimatroids, generalizing the previous connection between type-$A$ permutohedral varieties (Losev–Manin moduli spaces) and matroids, and the connection between type-$B$ permutohedral varieties and delta-matroids. Specifically, we equate a combinatorial nef cone of the moduli space with the space of ${\mathbb {R}}$-multimatroids, a generalization of multimatroids, and we introduce the independence polytopal complex of a multimatroid, whose volume is identified with an intersection number on the moduli space. As an application, we give a combinatorial formula for a natural class of intersection numbers on the moduli space by relating to the volumes of independence polytopal complexes of multimatroids.

中文翻译：

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多重拟阵和具有循环作用的有理曲线

我们研究了多重拟阵和具有循环作用的有理曲线模空间之间的联系。多重拟阵是拓扑图论中自然出现的拟阵和δ拟阵的推广。曲线模的视角为研究多重拟阵提供了一个热带框架，概括了先前$A$型全六面体簇（Losev-Manin模空间）与拟阵之间的联系，以及$B$型全六面体簇与δ-拟阵。具体来说，我们将模空间的组合 nef 锥与 ${\mathbb {R}}$-multimaroids 的空间等同起来，这是多阵的推广，并且我们引入了多阵的独立多面复形，其体积用模空间上的交集数。作为一个应用，我们通过与多拟阵的独立多面复形的体积相关，给出了模空间上自然类交集数的组合公式。