Riemann surfaces with a large abelian group of automorphisms

TL;DR

This paper classifies Riemann surfaces with large abelian automorphism groups, specifically those exceeding a size of 4(g-1), providing a comprehensive understanding of their structure.

Contribution

It offers a complete classification of Riemann surfaces with abelian automorphism groups larger than 4(g-1), extending previous results in the field.

Findings

Identified all Riemann surfaces with abelian automorphism groups exceeding 4(g-1)

Established bounds for the size of abelian automorphism groups

Provided explicit descriptions of these surfaces

Abstract

In this paper we classify all Riemann surfaces having a large abelian group of automorphisms, that is having an abelian group of automorphism of order strictly bigger then $4(g-1)$, where $g$ denotes as usual the genus of the Riemann surface.