论文标题
高属的加权稳定曲线的热带模量空间的拓扑
Topology of tropical moduli spaces of weighted stable curves in higher genus
论文作者
论文摘要
给定整数$ g \ geq 0 $，$ n \ geq 1 $和一个向量$ w \ in（\ mathbb {q} \ cap（0，1））^n $，以至于$ {2G -2 + \ 2 + \ sum w_i> 0} $第1卷。空间$δ_{g，w} $是Hassett的模量空间中的单数曲线的双重复合物，$ W $ stable $ g $ curves $ curves $ \ overline {\ mathcal {\ nathcal {m}}} $ W $。
Given integers $g \geq 0$, $n \geq 1$, and a vector $w \in (\mathbb{Q} \cap (0, 1])^n$ such that ${2g - 2 + \sum w_i > 0}$, we study the topology of the moduli space $Δ_{g, w}$ of $w$-stable tropical curves of genus $g$ with volume 1. The space $Δ_{g, w}$ is the dual complex of the divisor of singular curves in Hassett's moduli space of $w$-stable genus $g$ curves $\overline{\mathcal{M}}_{g, w}$. When $g \geq 1$, we show that $Δ_{g, w}$ is simply connected for all values of $w$. We also give a formula for the Euler characteristic of $Δ_{g, w}$ in terms of the combinatorics of $w$.
