Topology of tropical moduli spaces of weighted stable curves in higher genus
| Autor: | Kannan, Siddarth, Li, Shiyue, Serpente, Stefano, Yun, Claudia He |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $\Delta_{g, w}$ of $w$-stable tropical curves of genus $g$ with volume 1. The space $\Delta_{g, w}$ 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 $\Delta_{g, w}$ is simply connected for all values of $w$. We also give a formula for the Euler characteristic of $\Delta_{g, w}$ in terms of the combinatorics of $w$. Comment: 14 pages; 1 figure; final version accepted at Advances in Geometry |
| Databáze: | arXiv |
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