Some coverings defined over \(\mathbb{Q}\)
type: Item
instance of: scholarly article
title: Some coverings defined over \(\mathbb{Q}\)
zbMATH Open document ID: 0946.14015
DOI: 10.1007/BF02678203
author: Jean-Marc Couveignes
published in: Manuscripta Mathematica
publication date: 1997-09-04T00:00:00Z
full work available at URL: https://eudml.org/doc/156273
review text: This paper provides new examples that make explicit the Grothendieck correspondence between dessins d'enfants and Belyi pairs in some special cases. All examples are curves of genus 0 defined over \(\mathbb{Q}\), more precisely plane quadrics \(C_{m,n,p,q}\) depending on integer parameters \(m,n,p\) and \(q\), together with Belyi functions \(\lambda_{m,n,p,q}: C_{m,n,p,q} \to\mathbb{P}^1\). The author presents the corresponding (rather involved!) dessins by interpreting his curves as certain Hurwitz spaces and calculating the monodromy of the associated covering. He also studies in some detail the reduction of a plane quadric with integer coefficients at various primes; in particular he proves criteria for good and potentially good reduction of such a curve, and applies them to his examples.
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 14E20
Mathematics Subject Classification ID: 14H25
zbMATH DE Number: 1038275
zbMATH Keywords: ramified covering of \(\mathbb{P}^1-\{0,1,\infty\}\)
zbMATH Keywords: monodromy group
zbMATH Keywords: dessins d'enfants
zbMATH Keywords: Belyi pairs
reviewed by: Frank Herrlich
MaRDI profile type: Publication
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OpenAlex ID: W2320188208
description: scientific article; zbMATH DE number 1038275