Galois lines for the Giulietti–Korchmáros curve

Algebraic curves admitting inner and outer Galois points

“…(see [7]), where q is a power of p, P = (1 : 0 : 0) is an inner Galois point and Q = (0 : 1 : 0) is an outer Galois point ( [5]). However,…”

A birational embedding with two Galois points for certain Artin–Schreier curves

“…Let G 2 := ξG 1 ξ −1 , which fixes P 2 . According to [4], the 4-tuple (G 1 , G 2 , P 1 , P 2 ) satisfies conditions (a), (b) and (c).…”

“…Some known examples of plane curves with two Galois points are obtained as quotient curves C/H of curves C with a subgroup H ⊂ Aut(C) such that C has a birational embedding with two Galois points. Typical examples are quotient curves of the Hermitian curve ( [3,7]), and the Hermitian curve as a Galois subcover of the Giulietti-Korchmáros curve ( [2,4]).…”

Galois lines for the Artin-Schreier-Mumford curve

“…It is hard to solve this problem, even for well studied curves. The present author and Higashine determined the arrangement of all Galois lines for the Giulietti-Korchmáros curve ( [4]). However, this is only one known example of a curve in P 3 of degree d > 3 such that all Galois lines are determined (under the assumption that the automorphism group is non-trivial).…”