Genus Zero Actions on Riemann Surfaces

Details Genus Zero Actions on Riemann Surfaces Genus Zero Actions on Riemann Surfaces

1999-12-21

arxiv.org/abs/math/9912176v1

Mathematics

Algebraic Geometry

21 pages, 5 figures

Scientific paper

In this paper we determine all finite groups G that can act on some compact Riemann surface M with the property that if H is any non-trivial subgroup of G, then the orbit surface M/H is the Riemann sphere. The idea is to look at the induced action on the vector space of holomorphic differentials on M (in the positive genus case) and then use the old-known (Wolf) classification of groups admitting fixed point-free linear actions. A description of the corresponding group actions is given in terms of Fuchsian representations.

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