论文标题
曲线的热带模量空间的对称性
Symmetries of tropical moduli spaces of curves
论文作者
论文摘要
我们计算所有$ g，n \ geq 0 $ $ 3G -3 + n> 0 $，其中$ 3 + n> 0 $，其中$Δ__{g，n} \ n} \ subset m_ {g，n} $ g $和第一卷。特别是，我们表明$ \ mathrm {aut}（δ_{g}）$对于$ g \ geq 2 $是微不足道的，而$ \ mathrm {autrm {aut}（δ__{g，n}）\ cong s_n $当$ n \ geq 1 $ and $ n \ geq 1 $ and $（g，n）\ neq（g，n）\ neq（0，4），（1）从Chan，Galatius和Payne的意义上讲，空间$δ_{g，n} $是对称$δ$ - complex，并且在Deligne-Mumford-Knudsen Moduli Moduli Moduli Space $ \ edline $ \ edline {\ Mathcal {\ Mathcal {\ Mathcal {\ Mathcal {m} _ cervise {m} n and clignem-mumford-knudsen moduli moduli moduli moduli space中的双重交叉点n}在Massarenti的工作之后，他表明$ \ MATHRM {aut}（\ edline {\ Mathcal {m}} _ g）$对于$ g \ geq 2 $而言是微不足道的和$ 2G -2 + n \ geq 3 $，我们的结果意味着热带模量空间$δ_{g，n} $忠实地反映了代数模量空间的对称，用于一般$ g $和$ n $。
We compute the automorphism group $\mathrm{Aut}(Δ_{g, n})$ for all $g, n \geq 0$ such that $3g - 3 + n > 0$, where $Δ_{g, n} \subset M_{g, n}^\mathrm{trop}$ is the moduli space of stable $n$-marked tropical curves of genus $g$ and volume one. In particular, we show that $\mathrm{Aut}(Δ_{g})$ is trivial for $g \geq 2$, while $\mathrm{Aut}(Δ_{g, n}) \cong S_n$ when $n \geq 1$ and $(g, n) \neq (0, 4), (1, 2)$. The space $Δ_{g, n}$ is a symmetric $Δ$-complex in the sense of Chan, Galatius, and Payne, and is identified with the dual intersection complex of the boundary divisor in the Deligne-Mumford-Knudsen moduli space $\overline{\mathcal{M}}_{g, n}$ of stable curves. After the work of Massarenti, who has shown that $\mathrm{Aut}(\overline{\mathcal{M}}_g)$ is trivial for $g \geq 2$ while $\mathrm{Aut}(\overline{\mathcal{M}}_{g, n}) \cong S_n$ when $n \geq 1$ and $2g - 2 + n \geq 3$, our result implies that the tropical moduli space $Δ_{g, n}$ faithfully reflects the symmetries of the algebraic moduli space for general $g$ and $n$.
