Characterization of a Hermitian curve by Galois point

Abstract

For a plane curve, a point in the projective plane is said to be Galois when the point projection induces a Galois extension of function fields. We give a new characterization of a Fermat curve whose degree minus one is a power of $p$ in characteristic $p>2$, which is sometimes called Hermitian, by the number of Galois points lying on the curve.