Generating sets of Affine groups of low genus

TL;DR

This paper introduces a novel algorithm for computing braid orbits on Nielsen classes and applies it to classify all affine genus zero systems, which are coverings of the Riemann sphere with primitive affine monodromy groups.

Contribution

The paper presents a new algorithm for braid orbit computation and classifies all affine genus zero systems, advancing understanding of monodromy groups in algebraic geometry.

Findings

Algorithm successfully computes braid orbits on Nielsen classes.

Complete classification of affine genus zero systems achieved.

Identifies all coverings of the Riemann sphere with primitive affine monodromy groups.

Abstract

We describe a new algorithm for computing braid orbits on Nielsen classes. As an application we classify all families of affine genus zero systems; that is all families of coverings of the Riemann sphere by itself such that the monodromy group is a primitive affine permutation group.