Author

Nima Anvari

Date of Award

8-2009

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

Supervisor

Ian Hambleton

Language

English

Abstract

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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 g 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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