Symmetries of real cyclic \(p\)-gonal Riemann surfaces
type: Item
instance of: scholarly article
title: Symmetries of real cyclic \(p\)-gonal Riemann surfaces
zbMATH Open document ID: 1058.30033
author: Antonio F. Costas
author: Milagros Izquierdo
published in: Pacific Journal of Mathematics
publication date: 2004-11-01T00:00:00Z
review text: A symmetry of a compact Riemann surface \(X\) is an antiholomorphic involution \(\sigma:X\to X\). The paper under review deals with triples \((X,f,\sigma)\), where \(\sigma\) is a symmetry of the compact Riemann surface \(X\) and \(f:X\to\Sigma\) is a cyclic \(p\)-gonal morphism onto the Riemann sphere \(\Sigma\) such that \(f\circ\sigma= c\circ f\) where \(p\) is an odd prime and \(c:\Sigma\to\Sigma\) is complex conjugation. The main result of the paper which is carefully and very detailed proved by using the combinatorial theory of Riemann surfaces, is theorem 3, where the specia (i.e., the number of connected components of the fixed point set of \(\sigma\) and the orientability character of the quotient \(X/\langle \sigma\rangle)\) of all occuring symmetries \(\sigma\) of \(X\) are calculated.
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 20H10
zbMATH DE Number: 2113413
zbMATH Keywords: cyclic \(p\)-gonal covergin
zbMATH Keywords: symmetry
zbMATH Keywords: NEC group
zbMATH Keywords: species
reviewed by: Jose Manuel Gamboa
MaRDI profile type: Publication
full work available at URL: pjm.2004.213.231
OpenAlex ID: W2004630821
DOI: 10.2140/PJM.2004.213.231
description: scientific article; zbMATH DE number 2113413