# Topology of tropical moduli spaces of weighted stable curves in higher genus

@article{Kannan2020TopologyOT, title={Topology of tropical moduli spaces of weighted stable curves in higher genus}, author={Siddarth Kannan and Shiyue Li and Stefano Serpente and Claudia He Yun}, journal={arXiv: Combinatorics}, year={2020} }

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…

## 2 Citations

Filtrations of moduli spaces of tropical weighted stable curves

- Mathematics
- 2021

We consider tropical versions of Hassett’s moduli spaces of weighted stable curves M trop g,A , M trop g,A and ∆g,A associated to a weight datum A = (a1, ..., an) ∈ (Q∩ (0, 1]) n and study the…

Automorphisms of tropical Hassett spaces

- Mathematics
- 2021

Given an integer g ≥ 0 and a weight vector w ∈ Q∩(0, 1] satisfying 2g−2+ ∑ wi > 0, let ∆g,w denote the moduli space of n-marked, w-stable tropical curves of genus g and volume one. We calculate the…

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<p>We study the topology of a space <inline-formula content-type="math/mathml">
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