Multimatroids and Rational Curves with Cyclic Action
INTERNATIONAL MATHEMATICS RESEARCH NOTICES(2024)
摘要
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.
更多查看译文
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要