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

Abstract

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