Galois lines for the Giulietti--Korchm\'{a}ros curve

TL;DR

This paper characterizes all Galois lines for the Giulietti–Korchmarós curve in projective space and identifies Galois points for its plane model, revealing the curve's rich Galois structure.

Contribution

It provides a complete description of Galois lines for the GK curve and determines all Galois points for its plane model, a novel analysis in algebraic geometry.

Findings

All Galois lines for the GK curve are described.

The set of Galois points for the plane model is fully determined.

The GK curve has a large number of Galois points.

Abstract

We describe the arrangement of all Galois lines for the Giulietti--Korchm\'{a}ros curve in the projective $3$-space. As an application, we determine the set of all Galois points for a plane model of the GK curve. This curve possesses many Galois points.