Let be a smooth plane curve. A point in the projective plane is said to be Galois with respect to if the function field extension induced by the projection from is Galois. We denote by (resp. ) the number of Galois points contained in (resp. in ). In this article, we determine the numbers and in any remaining open cases. Summarizing results obtained by now, we will present a complete classification theorem of smooth plane curves by the number or . In particular, we give new characterizations of Fermat curve and Klein quartic curve by the number .
Cite this article
Satoru Fukasawa, Complete Determination of the Number of Galois Points for a Smooth Plane Curve. Rend. Sem. Mat. Univ. Padova 129 (2013), pp. 93–113DOI 10.4171/RSMUP/129-7