Galois points for a non-reflexive plane curve of low degree

Abstract

We consider a plane curve C. A point P in the projective plane is said to be Galois with respect to C if the projection from the point P induces a Galois extension of function fields. In this article, we give a new example of a plane curve C of degree q+1 such that the set of Galois points for C coincides with the one of Fq-rational points of P2. This curve appears in the classification list of ‘non-reflexive plane curves of low degree’ in positive characteristic. We also determine the sets of Galois points for such low-degree plane curves.