A topological construction of families of Galois covers of the line

Ghigi, Alessandro; Tamborini, Carolina

doi:10.2140/agt.2024.24.1569

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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

DOI: 10.2140/agt.2024.24.1569

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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Volume 24, issue 3 (2024)