Automorphisms of Riemann Surfaces
نویسنده
چکیده
This paper consists of mainly two parts. First it is a survey of some results on automorphisms of Riemann surfaces and Fuchsian groups. A theorem of Hurwitz states that the maximal automorphism group of a compact Riemann surface of genus 9 has order at most 84(g-1). It is well-known that the Klein quartic is the unique genus 3 curve that attains the Hurwitz bound. We will show in the second part of the paper that, in fact, the Klein curve is the unique non-singular curve in CP2 that attains the Hurwitz bound. The last section concerns automorphisms of surfaces with cusps or punctured surfaces.
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