An upper bound for the number of Galois points for a plane curve

Abstract

A point on a plane curve is said to be Galois (for the curve) if the projection from the point as a map from the curve to a line induces a Galois extension of function fields. It is known that the number of Galois points is finite except for a certain explicit example. We establish upper bounds for the number of Galois points for all plane curves other than the example in terms of the genus, degree and the generic order of contact, and settle curves attaining the bounds.

On the number of Galois points for a plane curve in characteristic zero

“…δ ′ (C) = 0, 1 or 3), and δ(C) = 4 (resp. δ ′ (C) = 3) if and only if C is projectively equivalent to the curve defined by present author gave an upper bound for δ(C) ( [3]); however, the bound is not sharp (in characteristic zero). Yoshihara conjectured the following ( [11]).…”