Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/9044
Title: | Automorphisms of Riemann Surfaces |
Authors: | Anvari, Nima |
Advisor: | Hambleton, Ian |
Department: | Mathematics and Statistics |
Keywords: | Mathematics;Statistics and Probability;Mathematics |
Publication Date: | Aug-2009 |
Abstract: | <p>p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times} span.s1 {font: 11.5px Helvetica}</p> <p>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.</p> |
URI: | http://hdl.handle.net/11375/9044 |
Identifier: | opendissertations/4202 5220 2031072 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Size | Format | |
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fulltext.pdf | 2.63 MB | Adobe PDF | View/Open |
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