Compact Riemann surfaces with large automorphism groups
type: Item
instance of: scholarly article
title: Compact Riemann surfaces with large automorphism groups
zbMATH Open document ID: 0933.30028
author: Takanori Matsuno
published in: Journal of the Mathematical Society of Japan
publication date: 2000-03-22T00:00:00Z
review text: Let \(X\) be a compact Riemann surface of genus \(g\geq 2\), having a finite Galois branched covering \(\pi : X \longrightarrow {\mathbb P}^1\). Denote the covering transformation group of \(\pi\) by \(\Aut (\pi)\). Then, \(\Aut (\pi)\) is a subgroup of \(\Aut (X)\), the automorphism group of \(X\). Assuming the order of \(\Aut (\pi)\) is greater than \(4(g-1)\), one can list up the possible branching indices of \(\pi\). In this paper the author divides these branching indices into two classes and shows that \(\Aut (X) =\) \(\Aut (\pi)\) always holds for the indices of one of the classes and not necessarily holds for those of another class.
Mathematics Subject Classification ID: 30F10
zbMATH DE Number: 1336920
zbMATH Keywords: branched covering
zbMATH Keywords: automorphism groups
zbMATH Keywords: compact Riemann surfaces
reviewed by: Takao Kato
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/05120309
OpenAlex ID: W1994750297
DOI: 10.2969/JMSJ/05120309
description: scientific article; zbMATH DE number 1336920