On \(F\)-data of automorphism groups of compact Riemann surfaces. The case of \(A_ 5\)
type: Item
instance of: scholarly article
title: On \(F\)-data of automorphism groups of compact Riemann surfaces. The case of \(A_ 5\)
zbMATH Open document ID: 0760.30019
author: Hideyuki Kimura
published in: Kodai Mathematical Journal
publication date: 1992-09-27T00:00:00Z
review text: Let \(X\) be a compact Riemann surface of genus \(g\geq 2\) and let \(\Aut(X)\) be the conformal automorphism group on \(X\). Since an automorphism induces a linear transformation of the space of holomorphic differentials on \(X\), there is a canonical representation \(\rho\) of \(\Aut(X)\to GL(g,\mathbb{C})\). In this paper, the author studies conditions for a subgroup \(A_ 5\) of \(GL(g,\mathbb{C})\) satisfying \(CY\)- and \(RH\)-conditions [for the definition, refer \textit{I. Kuribayashi}, Kodai Math. J. 7, 222-237 (1984; Zbl 0575.32025)] to be conjugate to the image under \(\rho\) of a subgroup of \(\Aut(X)\). To state these conditions, the author introduce a collection of nonnegative integers (which he called \(F\)-data in the title), inducing from characters of \(\rho\) and the fixed points of a subgroup of \(\Aut(X)\).
reviewed by: Takao Kato
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 30C20
Mathematics Subject Classification ID: 32M05
zbMATH DE Number: 60675
zbMATH Keywords: linear group
zbMATH Keywords: automorphism group
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039400
OpenAlex ID: W1981932388
cites work: Q5650865
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DOI: 10.2996/KMJ/1138039400
description: scientific article; zbMATH DE number 60675