论文标题
Teichmüller空间及其热带化的非架构类似物
A non-Archimedean analogue of Teichmüller space and its tropicalization
论文作者
论文摘要
在本文中，我们使用来自热带和对数几何形状的技术来构建TeichMüller空间的非架构类似物$ \上线{\ Mathcal {t}} _ g $，其点成对是由非Archimedean Field和Teichmüllllerer的稳定的投射曲线组成的稳定的投射曲线，并具有teichmüllllerer的分析库，该组成的组成部分是构成的。这种结构与Gerritzen和Herrlich的Mumford Curves的非架构Schottky空间的经典结构密切相关和启发。我们认为，非ArchimedeanTeichmüller空间的骨骼恰恰是Chan-Melo-Viviani引入的热带Teichmüller空间，这是Culler-Vogtmann外层空间的简单完成。结果，外太空事实证明是在$ \ overline {\ Mathcal {t}} _ g $中平滑mumford曲线轨迹轨迹的强烈变形缩回。
In this article we use techniques from tropical and logarithmic geometry to construct a non-Archimedean analogue of Teichmüller space $\overline{\mathcal{T}}_g$ whose points are pairs consisting of a stable projective curve over a non-Archimedean field and a Teichmüller marking of the topological fundamental group of its Berkovich analytification. This construction is closely related to and inspired by the classical construction of a non-Archimedean Schottky space for Mumford curves by Gerritzen and Herrlich. We argue that the skeleton of non-Archimedean Teichmüller space is precisely the tropical Teichmüller space introduced by Chan-Melo-Viviani as a simplicial completion of Culler-Vogtmann Outer space. As a consequence, Outer space turns out to be a strong deformation retract of the locus of smooth Mumford curves in $\overline{\mathcal{T}}_g$.
