Nonequivalent coverings of Riemann surfaces with a prescribed ramification type
type: Item
instance of: scholarly article
title: Nonequivalent coverings of Riemann surfaces with a prescribed ramification type
zbMATH Open document ID: 0598.30058
DOI: 10.1007/BF00968900
published in: Siberian Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: Continuing his investigation [Dokl. Akad. Nauk SSSR 239, 269-271 (1978; Zbl 0395.30034); ibid. 244, 529-532 (1979; Zbl 0416.30038)], the author gives complete proofs for theorems that he announced in a previous paper [ibid. 261, 537-542 (1981; Zbl 0506.30031)] and gives in terms of irreducible representations of symmetric groups a complete solution of the A. Hurwitz problem on the number of topologically nonequivalent coverings of a compact Riemann surface of genus p with a given type of ramification. In these same terms, he gives for every p necessary and sufficient conditions for the existence of such coverings and shows that asymptotically almost all coverings with a fixed type of ramification have a trivial group of transformations of the covering. See also a paper by \textit{H. Röhrl} [Trans. Am. Math. Soc. 107, 320-346 (1963; Zbl 0115.067)].
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 30F25
Mathematics Subject Classification ID: 30C25
zbMATH DE Number: 3964349
author: Alexander Mednykh
MaRDI profile type: Publication
cites work: Riemann surface transformation groups
cites work: Q4177833
cites work: Q3205528
cites work: Branch Point Structure of Covering Maps Onto Nonorientable Surfaces
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cites work: Q5631018
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cites work: Q5651924
cites work: Fields of definition of function fields and hurwitz families — groups as galois groups
cites work: Über das Hurwitzsche Problem der Bestimmung der Anzahl Riemannscher Flächen von gegebener Verzweigungsart
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description: scientific article; zbMATH DE number 3964349