JournalsrsmupVol. 129pp. 93–113

Complete Determination of the Number of Galois Points for a Smooth Plane Curve

  • Satoru Fukasawa

    Yamagata University, Japan
Complete Determination of the Number of Galois Points for a Smooth Plane Curve cover
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Abstract

Let CC be a smooth plane curve. A point PP in the projective plane is said to be Galois with respect to CC if the function field extension induced by the projection from PP is Galois. We denote by δ(C){\delta} (C) (resp. δ(C){\delta} '(C)) the number of Galois points contained in CC (resp. in P2C{\mathbb P}^2 \setminus C). In this article, we determine the numbers δ(C){\delta} (C) and δ(C){\delta} '(C) in any remaining open cases. Summarizing results obtained by now, we will present a complete classification theorem of smooth plane curves by the number δ(C){\delta} (C) or δ(C){\delta} '(C). In particular, we give new characterizations of Fermat curve and Klein quartic curve by the number δ(C){\delta} '(C).

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. 93–113

DOI 10.4171/RSMUP/129-7