Isometry Groups of Compact Riemann Surfaces
نویسندگان
چکیده
We explore the structure of compact Riemann surfaces by studying their isometry groups. First we give two constructions due to Accola [1] showing that for all g ≥ 2, there are Riemann surfaces of genus g that admit isometry groups of at least some minimal size. Then we prove a theorem of Hurwitz giving an upper bound on the size of any isometry group acting on any Riemann surface of genus g ≥ 2. Finally, we briefly discuss Hurwitz surfaces – Riemann surfaces with maximal symmetry – and comment on a method for computing isometry groups of Riemann surfaces.
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