Faithful tropicalization and Skeleton of $\overline{M}_{0,n}$

TL;DR

This paper demonstrates that the Berkovich skeleton of the analytification of ,n and its faithful tropicalization are combinatorially identical in terms of valuation, linking non-Archimedean geometry with tropical geometry.

Contribution

It establishes the equivalence between the Berkovich skeleton and faithful tropicalization of ,n, providing a new understanding of their combinatorial structure.

Findings

The Berkovich skeleton and faithful tropicalization are the same in valuation terms.

The combinatorial structures of ,n are explicitly compared and shown to coincide.

The results bridge non-Archimedean and tropical geometries for moduli spaces.

Abstract

We propose a comparison between the Berkovich skeleton of Berkovich analytification of $(\overline{\textsf{M}}_{0,n},{\overline{\textsf{M}}_{0,n} \setminus \textsf{M}_{0,n}})$ and faithful tropicalization of $\textsf{M}_{0,n}$ over a complete discrete valued field. In particular, we proved the two combinatorial structures are the same in terms of valuation in $\overline{\textsf{M}}^{\textsf{an}}_{0,n}$.