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arXiv · 1011.3648

Complete determination of the number of Galois points for a smooth plane curve

Satoru Fukasawa
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Abstract

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

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Satoru Fukasawa. 2011-06-29. Complete determination of the number of Galois points for a smooth plane curve. https://arxiv.org/abs/1011.3648

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