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.

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.