# Tropical moduli spaces of stable maps to a curve

## TL;DR

This paper constructs tropical moduli spaces of rational stable maps to a smooth tropical curve in R^r, describing their structure as tropical varieties with weights determined by lattice indices and Hurwitz numbers.

## Contribution

It introduces a new construction of tropical moduli spaces for rational stable maps to arbitrary smooth tropical curves, expanding the understanding of their geometric and combinatorial properties.

## Key findings

- Moduli spaces are realized as tropical varieties within balanced fans.
- Weights are explicitly computed using lattice indices and local Hurwitz numbers.
- The construction applies to arbitrary smooth tropical curves in R^r.

## Abstract

We construct moduli spaces of rational covers of an arbitrary smooth tropical curve in R^r as tropical varieties. They are contained in the balanced fan parametrizing tropical stable maps of the appropriate degree to R^r. The weights of the top-dimensional polyhedra are given in terms of certain lattice indices and local Hurwitz numbers.