An English translation of A. Wiman's "On the algebraic curves of genus $p=4$, $5$ and $6$, which posses unambiguous transformations into themselves"

TL;DR

This paper classifies algebraic curves of genus 4, 5, and 6 with non-trivial automorphisms, providing a comprehensive analysis of their symmetries using classical algebraic geometry techniques.

Contribution

It offers the first English translation of Wiman's 1895 work, detailing the classification of algebraic curves with automorphisms for specific genera.

Findings

Classification of non-hyperelliptic curves with automorphisms

Identification of automorphism groups for genus 4, 5, and 6

Use of classical algebraic geometry methods

Abstract

This is an English translation of the paper "Ueber die algebraischen Curven von den Geschlechtern $p = 4$, $5$ und $6$, welche eindeutigen Transformationen in sich besitzen" by Anders Wiman, Bihang till Kongl. Svenska vetenskaps-akademiens handlingar 21 (1895): 1-41. The article, originally written in German, classifies non-hyperelliptic curves which have non-trivial automorphism groups via classical methods in algebraic geometry.