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 completely classify plane curves with infinitely many outer Galois points.
"Classification of plane curves with infinitely many Galois points." J. Math. Soc. Japan 63 (1) 195 - 209, January, 2011. https://doi.org/10.2969/jmsj/06310195