论文标题
Riemann表面热带化的模量空间
The moduli space of the tropicalizations of Riemann surfaces
论文作者
论文摘要
在本文中，我们研究了Riemann表面热带化的模量空间。我们首先通过由（双曲线）对裤子分解定义的图表对光滑的指向的riemann表面进行热带化。然后，我们可以基于固定的常规热带化构建热带化的模量空间，并通过添加层次参数化的加权收缩来压缩它。我们表明，这个紧凑的模量空间也是Hausdorff。最后，我们将这个模量空间与Riemann表面的模量空间进行了比较，并在这两个模量空间的分层之间建立了部分订单保留的对应关系。
In this paper we study the moduli space of the tropicalizations of Riemann surfaces. We first tropicalize a smooth pointed Riemann surface by a graph defined by its (hyperbolic) pair of pants decomposition. Then we can construct the moduli space of tropicalizations based on a fixed regular tropicalization, and compactify it by adding strata parametrizing weighted contractions. We show that this compact moduli space is also Hausdorff. In the end, we compare this moduli space with the moduli space of Riemann surfaces, establishing a partial order-preserving correspondence between the stratifications of these two moduli spaces.
