A matrix representation for automorphisms of compact Riemann surfaces

Automorphisms of Riemann Surfaces

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 par...

Prime Order Automorphisms of Riemann Surfaces

Recently there has been renewed interest in the mappingclass group of a compact surface of genus g ≥ 2 and also in its finite order elements. A finite order element of the mapping-class group will be a conformal automorphism on some Riemann surface of genus g. Here we give the details of the proof that there is an adapted basis for any conformal automorphism of prime order on a surface of genus...

Notes on Compact Riemann Surfaces

Introduction to Compact Riemann Surfaces

The theory of Riemann surfaces is a classical field of mathematics where geometry and analysis play equally important roles. The purpose of these notes is to present some basic facts of this theory to make this book more self contained. In particular we will deal with classical descriptions of Riemann surfaces, Abelian differentials, periods on Riemann surfaces, meromorphic functions, theta fun...

Ela Dihedral Groups of Automorphisms of Compact Riemann Surfaces of Genus Two

In this short note, the conjugacy classes of finite dihedral subgroups of the 4 × 4 integral symplectic group are considered. A complete list of representatives of the classes is obtained, among them six classes are realizable by analytic automorphisms of compact connected Riemann surfaces of genus two.