Berkovich spaces and Deligne-Mumford compactification

TL;DR

This paper explores the connection between Berkovich spaces and the Deligne-Mumford compactification, revealing how dynamics on the Berkovich projective line relate to the moduli space of marked spheres.

Contribution

It explicitly establishes the relationship between Berkovich dynamics and the Deligne-Mumford compactification through the space of trees of spheres.

Findings

Berkovich projective line dynamics correspond to trees of spheres.

The work clarifies the link between non-Archimedean geometry and moduli space compactification.

Provides a framework for understanding dynamics in algebraic geometry.

Abstract

We explicit the relation between the dynamics the Berkovich projective line over the completion of the field of formal Puiseux series and the space dynamical systems between trees of spheres known to be equivalent to the Deligne-Mumford compactification of the Moduli space of marked spheres.