Wonderful compactifications and rational curves with cyclic action

TL;DR

This paper demonstrates that a moduli space of rational curves with cyclic symmetry can be realized as a wonderful compactification, linking it to toric varieties and enabling Chow ring computations.

Contribution

It establishes a new realization of the moduli space as a wonderful compactification and connects it to explicit toric varieties, providing computational tools.

Findings

Moduli space is Chow-equivalent to an explicit toric variety.

The paper provides a general result on wonderful compactifications.

Chow ring of the moduli space can be explicitly computed.

Abstract

We prove that the moduli space of rational curves with cyclic action, constructed in our previous work, is realizable as a wonderful compactification of the complement of a hyperplane arrangement in a product of projective spaces. By proving a general result on such wonderful compactifications, we conclude that this moduli space is Chow-equivalent to an explicit toric variety (whose fan can be understood as a tropical version of the moduli space), from which a computation of its Chow ring follows.