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A topological construction of families of Galois covers of the line

Alessandro Ghigi and Carolina Tamborini

Algebraic & Geometric Topology 24 (2024) 1569–1600
Abstract

We describe a new construction of families of Galois coverings of the line using basic properties of configuration spaces, covering theory, and the Grauert–Remmert extension theorem. Our construction provides an alternative to a previous construction due to González-Díez and Harvey (which uses Teichmüller theory and Fuchsian groups) and, in the case the Galois group is nonabelian, corrects an inaccuracy therein. In the opposite case where the Galois group has trivial center, we recover some results due to Fried and Völklein.

Keywords
configuration spaces, moduli spaces of curves, coverings, braid groups, mapping class groups
Mathematical Subject Classification
Primary: 20F36, 32G15, 32J25, 57K20
References
Publication
Received: 16 April 2022
Revised: 5 October 2022
Accepted: 2 December 2022
Published: 28 June 2024
Authors
Alessandro Ghigi
Università degli Studi di Pavia
Pavia
Italy
Carolina Tamborini
Universiteit Utrecht
Utrecht
Netherlands

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