Proceedings of the Japan Academy, Series A, Mathematical Sciences

Automorphism group of plane curve computed by Galois points, II

Takeshi Harui, Kei Miura, and Akira Ohbuchi

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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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 94, Number 6 (2018), 59-63.

Dates
First available in Project Euclid: 31 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.pja/1527732017

Digital Object Identifier
doi:10.3792/pjaa.94.59

Subjects
Primary: 14H37: Automorphisms
Secondary: 14H50: Plane and space curves

Keywords
Icosahedral group Galois point plane curve automorphism group

Citation

Harui, Takeshi; Miura, Kei; Ohbuchi, Akira. Automorphism group of plane curve computed by Galois points, II. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 6, 59--63. doi:10.3792/pjaa.94.59. https://projecteuclid.org/euclid.pja/1527732017


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References

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