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arXiv · 1709.05025

Automorphism group of plane curve computed by Galois points, II

Takeshi Harui·Kei Miura·Akira Ohbuchi
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Abstract

Recently, the first author classified finite groups obtained as automorphism groups of smooth plane curves of degree $d \ge 4$ into five types. He gave an upper bound of the order of the automorphism group for each types. For one of them, the type (a-ii), that is given by $\max \left\{ 2 d (d - 2), 60 d \right\}$. In this article, we shall construct typical examples of smooth plane curve $C$ by applying the method of Galois points, whose automorphism group has order $60 d$. In fact, we determine the structure of the automorphism group of those curves.

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Takeshi Harui, Kei Miura, Akira Ohbuchi. 2017-09-15. Automorphism group of plane curve computed by Galois points, II. https://arxiv.org/abs/1709.05025

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