Die Automorphismengruppen hyperelliptischer Kurven. (The groups of automorphisms of hyperelliptic curves)
type: Item
instance of: scholarly article
title: Die Automorphismengruppen hyperelliptischer Kurven. (The groups of automorphisms of hyperelliptic curves)
zbMATH Open document ID: 0588.14022
DOI: 10.1007/BF01168614
author: Rolf Brandt
author: Henning Stichtenoth
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155128
review text: Let \(\Gamma\) be a hyperelliptic curve over an algebraically closed field of characteristic 0 and G a group of automorphisms of \(\Gamma\) containing the canonical involution. The authors study the group theoretic structure of G and relate it to the ramification behavior of the morphism \(p:\quad \Gamma \to \Gamma /G.\) Using the well known classification of finite subgroups of PGL(2,\({\mathbb{C}})\), they first obtain a classification of the possible ramification types of p. The computation of the number of involutions in G then shows the main result (theorem 5.1): Up to isomorphism, G depends only on the ramification type of p. Actually, the authors do much more: For each type, the corresponding group is determined, and a way to obtain normal forms is indicated. The proofs use complicated case by case considerations which are carried out only in typical special cases.
reviewed by: Ernst-Ulrich Gekeler
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14H30
zbMATH DE Number: 3944023
zbMATH Keywords: hyperelliptic curve
zbMATH Keywords: characteristic 0
zbMATH Keywords: group of automorphisms
zbMATH Keywords: ramification
MaRDI profile type: Publication
cites work: On solvable extensions of algebraic number fields
cites work: Q3882615
cites work: On conformal mapping of a hyperelliptic Riemann surface onto itself
OpenAlex ID: W2060809315
description: scientific article; zbMATH DE number 3944023