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

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 $\overline{\textsf{M}}^{\textsf{an}}_{0,n}$.