Automorphismen und Modulraum Galoisscher dreiblättriger Überlagerungen
type: Item
instance of: scholarly article
title: Automorphismen und Modulraum Galoisscher dreiblättriger Überlagerungen
zbMATH Open document ID: 0573.32020
DOI: 10.1007/BF01168832
author: Andrei Duma
author: Wolfgang Radtke
published in: Manuscripta Mathematica
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155055
review text: Let \(M_ g\) denote the space of isomorphism classes of compact Riemann surfaces of genus g. Consider the subset \(M^ 3_ g\) of \(M_ g\) which consists of those Riemann surfaces that admit a threefold Galois cover over \({\mathbb{P}}^ 1\). In this work the space \(M^ 3_ g\) is parametrized using branch points of the Galois covers. It turns out that \(M^ 3_ 3\) is connected but for \(g>3\) \(M^ 3_ g\) is not connected. The authors give a formula for the number of components of a general \(M^ 3_ g\) and give rather explicit descriptions of them as well. The paper ends with a list of the automorphism groups of certain threefold Galois covers of \({\mathbb{P}}^ 1\) of genus g for \(g=3,4,5,6\).
Mathematics Subject Classification ID: 32G13
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 30F99
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 32G15
zbMATH DE Number: 3914709
zbMATH Keywords: moduli spaces
zbMATH Keywords: Weierstrass-points
zbMATH Keywords: automorphism groups of Riemann surfaces
zbMATH Keywords: threefold Galois cover
reviewed by: Mika Seppälä
MaRDI profile type: Publication
cites work: Q3931656
cites work: Q4161928
cites work: Q4052265
description: scientific article; zbMATH DE number 3914709