Notes on classification of Riemann surfaces

Notes on Compact Riemann Surfaces

Topological Classification of Conformal Actions on pq-Hyperelliptic Riemann Surfaces

A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if X admits a conformal involution ρ for which X/ρ is an orbifold of genus p. Here we classify conformal actions on 2-hyperelliptic Rieman surfaces of genus g > 9, up to topological conjugacy and determine which of them can be maximal.

Computing on Riemann Surfaces

These notes are a review on computational methods that allow us to use computers as a tool in the research of Riemann surfaces, algebraic curves and Jacobian varieties. It is well known that compact Riemann surfaces, projective algebraiccurves and Jacobian varieties are only diierent views to the same object, i.e., these categories are equivalent. We want to be able to put our hands on this equ...

Coalescence on Riemann Surfaces

We consider coalescing fermions on a Riemann Surface and derive generalized determinant formulas, complementing some results of 3].

Riemann Surfaces: Expanded Notes for a 25 Minute Talk

These are some notes that I collected from my readings about Riemann surfaces. Most of the notes are based on Beardon’s book Primer on Riemann Surfaces. These notes will serve as my lecture notes for a 25 minute talk I am giving in my Algebraic Topology class. I was not able to cover the last section during the talk.