# Moduli spaces of rational tropical curves

## TL;DR

This paper defines and studies the moduli spaces of rational tropical curves with marked points, establishing their structure as smooth tropical varieties and introducing their compactifications and divisor classes.

## Contribution

It introduces the moduli space of rational tropical curves, proves its smooth tropical variety structure, and constructs its Deligne-Mumford compactification and tropical psi-class divisors.

## Key findings

- Moduli space has a smooth tropical variety structure of dimension n-3.
- Defined the Deligne-Mumford compactification for these spaces.
- Introduced tropical psi-class divisors on the moduli space.

## Abstract

This note is devoted to the definition of moduli spaces of rational tropical curves with n marked points. We show that this space has a structure of a smooth tropical variety of dimension n-3. We define the Deligne-Mumford compactification of this space and tropical $\psi$-class divisors.