Families of finite coverings of the Riemann sphere
The paper under review deals with coverings of the projective line, in particular with \((G,H)\)-coverings, i.e. coverings whose permutation monodromy representation is equivalent to that of the group \(G\) on the set of left cosets \(G/H\) (the subgroup \(H\) here does not contain any non-trivial normal subgroup of \(G\)). For fixed \(G\) and \(H\) the authors define a \textsl{Hurwitz family} a non-degenerate family of \((G,H)\)-coverings containing all such coverings topologically equivalent to a given one such that different members of it are not isomorphic. They discuss the problem of the existence of such families and give a criterion in some special cases.
scientific article; zbMATH DE number 6005137
scientific article