Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$

TL;DR

This paper provides an explicit parameter space for all quadratic rational maps on the projective line over a field, classified up to conjugacy, facilitating better understanding and classification of such maps.

Contribution

It introduces a detailed parameter space for quadratic maps on  over a field, explicitly characterizing their conjugacy classes.

Findings

Explicit parameter space constructed for quadratic maps

Classification up to conjugacy over the field $K$

Enhanced understanding of quadratic rational maps

Abstract

We describe an explicit parameter space for the set of all quadratic rational maps on $\pp^1$ defined over a field $K$, up to conjugacy over $K$.