• Corpus ID: 225040139

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… 
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TLDR
A tropical analogue of Hassett's moduli spaces of weighted stable curves is defined and it is shown that the naive set-theoretic tropicalization map can be identified with a natural deformation retraction onto the non-Archimedean skeleton.
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<p>We study the topology of a space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Delta Subscript g"> <mml:semantics>
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