Homology, Belyĭfunctions and canonical curves
type: Item
instance of: scholarly article
title: Homology, Belyĭfunctions and canonical curves
zbMATH Open document ID: 0887.14013
DOI: 10.1007/BF02568321
published in: Manuscripta Mathematica
publication date: 1997-04-08T00:00:00Z
full work available at URL: https://eudml.org/doc/156208
review text: After a brief review of maps, hypermaps and Belyi function, the author studies a linear representation of the automorphism group of a Riemann surface \(X\) generated by elements \(\alpha_1, \alpha_2, \alpha_3: =(\alpha_1 \alpha_2)^{-1}\). Then he applies the results obtained to the representation of the automorphism group of a Riemann surface on its abelian differentials \(\Omega(X)\) of the first kind, and gets relations among the multiplicities of the eigenvalues of the representation matrix, the degree of the irreducible representation, the number of its occurring times in the representation on \(\Omega(X)\) and the orders of \(\alpha_i\). As examples, the calculations of the representation for several groups are given. The author also mentions the canonical curve \(C(X)\) of \(X\), and the informations at the fixed points on \(C(X)\) of the automorphisms \(\alpha_1, \alpha_2, \alpha_3\) is used to find the equations corresponding to a given map.
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14E07
Mathematics Subject Classification ID: 30F30
Mathematics Subject Classification ID: 14H30
zbMATH DE Number: 980710
zbMATH Keywords: hypermaps
zbMATH Keywords: Belyi function
zbMATH Keywords: automorphism group of a Riemann surface
zbMATH Keywords: canonical curve
zbMATH Keywords: fixed points
author: Manfred Streit
reviewed by: Ryutaro Horiuchi
describes a project that uses: GAP
MaRDI profile type: Publication
cites work: ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD
cites work: Q4325460
cites work: Regular hypermaps
cites work: Q4325462
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cites work: Finitely Maximal Fuchsian Groups
OpenAlex ID: W2006104417
description: scientific article; zbMATH DE number 980710