On an algebraization of the Riemann-Hurwitz relation
type: Item
instance of: scholarly article
title: On an algebraization of the Riemann-Hurwitz relation
zbMATH Open document ID: 0575.32025
author: Izumi Kuribayashi
published in: Kodai Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: The author studies the canonical representation Aut(M)\(\to GL(g,C)\) with the space of holomorphic differentials on M as its representation module, where M is a compact Riemann surface of genus\(\geq 2\). For an automorphism group AG of M, let R(M,AG) be its image. The GL(g,C)-conjugate class of R(M,AG) appears as an invariant of the holomorphic family of Riemann surfaces which is defined by the subgroup of Teichmüller modular group corresponding to the pair (M,AG). In this paper the author proves two necessary conditions for a finite subgroup of GL(g,C) to be conjugate to some R(M,AG). When \(g=2\) they are also sufficient conditions.
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 14H99
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 30F35
zbMATH DE Number: 3918810
zbMATH Keywords: conformal automorphism group
zbMATH Keywords: Eichler trace formula
zbMATH Keywords: Riemann-Hurwitz relation
zbMATH Keywords: compact Riemann surface
reviewed by: Takao Kato
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138036909
OpenAlex ID: W2041374600
cites work: On the Number of Automorphisms of a Closed Riemann Surface
cites work: Q3855356
cites work: Q3931656
cites work: Holomorphic families of compact Riemann surfaces with automorphisms
cites work: On certain curves of genus three with many automorphisms
cites work: On automorphisms of prime order of a Riemann surface as matrices
DOI: 10.2996/KMJ/1138036909
Recommended article: Q3780130
Recommended article: The algebra of Hurwitz multizeta functions
Recommended article: From the algebras of Riemann polyzetas to the algebra of Hurwitz polyzetas
Recommended article: The relative Riemann–Hurwitz formula
Recommended article: Note on algebraic irregular Riemann-Hilbert correspondence
Recommended article: A Riemann–Hurwitz Theorem for the Algebraic Euler Characteristic
Recommended article: Q5311087
Recommended article: Q5173377
Recommended article: Algebras of differentiable functions on Riemann surfaces
Recommended article: On algebraic relations for Ramanujan's functions
description: scientific article; zbMATH DE number 3918810