Uniformization of surfaces of genus two with automorphisms
type: Item
instance of: scholarly article
title: Uniformization of surfaces of genus two with automorphisms
zbMATH Open document ID: 0663.14020
DOI: 10.1007/BF01457012
author: Gonzalo Riera
author: Rubí E. Rodríguez
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164449
review text: Let C be a Riemann surface of genus two admitting an involution besides the hyperelliptic one (which is denoted by i), and consider the tori obtained as quotients of C by \(<\sigma >\) and by \(<i\sigma >\). The authors completely describe the relations occurring among the non euclidean polygons uniformizing C, the Riemann matrix of C and the equations of the tori above. When C is described as a quartic with a double point, some geometrical property of bitangents of C is proven. Finally, for each possible group automorphisms of C the corresponding polygon is characterized.
reviewed by: Cristina Turrini
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 4083805
zbMATH Keywords: uniformization
zbMATH Keywords: Riemann surface of genus two
zbMATH Keywords: involution
zbMATH Keywords: Riemann matrix
zbMATH Keywords: group automorphisms
MaRDI profile type: Publication
cites work: Q3310101
cites work: Theta functions and non-linear equations
cites work: Arithmetic variety of moduli for genus two
cites work: On algebraic curves (of low genus) defined by Kleinian groups
cites work: Riemann surfaces and the theta function
cites work: The Fenchel-Nielsen deformation
cites work: Q3931656
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description: scientific article; zbMATH DE number 4083805