Automorphism group of plane curve computed by Galois points, II

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Takeshi Harui¹  Kei Miura²  Akira Ohbuchi³ 

[1] Department of Core Studies, Kochi University of Technology;Department of Mathematics, National Institute of Technology, Ube College;Department of Mathematical Sciences, Faculty of Science and Technology, Tokushima University

关键词: Icosahedral group;    Galois point;    plane curve;    automorphism group.;   

DOI  :  10.3792/pjaa.94.59

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

Recently, the first author~[3] 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 $\max \{2d (d - 2), 60 d\}$. 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 $60d$. In fact, we determine the structure of the automorphism group of those curves.

【 授权许可】

Unknown