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June 2018 Automorphism group of plane curve computed by Galois points, II
Takeshi Harui, Kei Miura, Akira Ohbuchi
Proc. Japan Acad. Ser. A Math. Sci. 94(6): 59-63 (June 2018). DOI: 10.3792/pjaa.94.59

Abstract

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.

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Takeshi Harui. Kei Miura. Akira Ohbuchi. "Automorphism group of plane curve computed by Galois points, II." Proc. Japan Acad. Ser. A Math. Sci. 94 (6) 59 - 63, June 2018. https://doi.org/10.3792/pjaa.94.59

Information

Published: June 2018
First available in Project Euclid: 31 May 2018

zbMATH: 06941823
MathSciNet: MR3808538
Digital Object Identifier: 10.3792/pjaa.94.59

Subjects:
Primary: 14H37
Secondary: 14H50

Keywords: automorphism group , Galois point , Icosahedral group , plane curve

Rights: Copyright © 2018 The Japan Academy

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Vol.94 • No. 6 • June 2018
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