On the topology of the moduli of tropical unramified p-covers

Autor:	Maazouz, Yassine El, Helminck, Paul Alexander, Röhrle, Felix, Souza, Pedro, Yun, Claudia He
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry Mathematics - Algebraic Topology Mathematics - Combinatorics 14T20 05E14 14H10
Druh dokumentu:	Working Paper
Popis:	We study the topology of the moduli space of unramified $\mathbb{Z}/p$-covers of tropical curves of genus $g \geq 2$, where $p$ is a prime number. We use recent techniques by Chan--Galatius--Payne to identify contractible subcomplexes of the moduli space. We then use this contractibility result to show that this moduli space is simply connected. In the case of genus 2, we determine the homotopy type of this moduli space for all primes $p$. This work is motivated by prospective applications to the top-weight cohomology of the space of prime cyclic \'etale covers of smooth algebraic curves. Comment: 39 pages, 11 figures, 5 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.06624 Zobrazit plný text záznamu View this record from Arxiv