Finite degree holomorphic covers of compact Riemann surfaces
type: Item
instance of: scholarly article
title: Finite degree holomorphic covers of compact Riemann surfaces
zbMATH Open document ID: 1105.14035
author: Jouni Parkkonen
author: Vesa Ruuska
publication date: 2006-12-13T00:00:00Z
review text: Let \(X_1, X_2\) be compact Riemann surfaces and \(K>1\). Here the authors prove the existence of an arithmetic Riemann surface \(Y\) (i.e. a Riemann surface defined over an algebraic field) and finite degree \(K\)-quasiregular maps \(r_i: Y \to X_i\), \(i=1,2\), which are unbranched outside the preimages of \(\{0,1,\infty \}\) by a Belyi map. They also prove the existence of branched ramified covering \(Z_i \to X_i\), \(i=1,2\), such that there is a \(K\)-quasiconformal homeomorphism \(Z_1 \to Z_2\). The latter result is an asymptotic form of a conjecture of Ehrenpreis which states that \(X_1, X_2\) have finite degree unbranched coverings which are arbitrarly near in the common moduli space. The authors discuss the full conjecture and give more results on arithmetic curves.
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14H15
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 32G15
zbMATH DE Number: 5080002
zbMATH Keywords: covering maps
zbMATH Keywords: quasiconformal maps
zbMATH Keywords: arithmetic algebraic curves
Wikidata QID: Q110022012
MaRDI profile type: Publication
full work available at URL: s10114-005-0824-x
OpenAlex ID: W2080356911
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DOI: 10.1007/S10114-005-0824-X
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5080002