Smooth covers of moduli stacks of Riemann surfaces with symmetry

Perroni, Fabio

doi:10.1007/s40574-021-00284-7

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The Group Aut1

Introduction1

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2022

2024

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Cited by 4 publications

(2 citation statements)

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“…These "universal" families have been widely studied and used in the literature for several purposes in the last decades, see e.g. [1,7,8,9,31,15,17,18,33,35,41]. They were first constructed by González-Díez and Harvey [21] using Teichmüller theory.…”

Section: The Group Autmentioning

confidence: 99%

Topological types of actions on curves

Conti¹,

Ghigi²,

Pignatelli³

2022

Preprint

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Section: The Group Autmentioning

confidence: 99%

Topological types of actions on curves

Conti¹,

Ghigi²,

Pignatelli³

2022

Preprint

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“…This result has been subsequently used in several papers, e.g. [2,6,7,19,20], just to mention a few.…”

Section: Introductionmentioning

confidence: 98%

A topological construction of families of Galois covers of the line

Ghigi¹,

Tamborini²

2022

Preprint

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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 non-abelian, corrects an inaccuracy therein. Contents 1. Introduction 1 2. Configuration spaces 4 3. Parallel transport 5 4. Dehn-Nielsen theorems and consequences 6 5. Topological types of actions 9 6. Tools for the construction 12 7. Construction of the families of G-curves 15 8. Independence from the choices 18 9. The abelian case 22 References 23

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