Open Access
October 2022 Smooth plane curves with outer Galois points whose reduced automorphism group is $A_{5}$
Takeshi Harui, Kei Miura, Akira Ohbuchi
Proc. Japan Acad. Ser. A Math. Sci. 98(8): 67-71 (October 2022). DOI: 10.3792/pjaa.98.013

Abstract

In [8] the first author classified automorphism groups of smooth plane curves of degree not less than four into five types. If the curve has a unique outer Galois point, then the quotient group of its automorphism group by the Galois group at the point, which is called the reduced automorphism group, is a finite subgroup of one-dimensional projective linear group. This article is a sequel of [10] and [9]. In this article, we shall determine the defining equation of the curve when the reduced automorphism group is an icosahedral group and give a description of the full automorphism group.

Citation

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Takeshi Harui. Kei Miura. Akira Ohbuchi. "Smooth plane curves with outer Galois points whose reduced automorphism group is $A_{5}$." Proc. Japan Acad. Ser. A Math. Sci. 98 (8) 67 - 71, October 2022. https://doi.org/10.3792/pjaa.98.013

Information

Published: October 2022
First available in Project Euclid: 29 September 2022

MathSciNet: MR4492080
zbMATH: 1502.14077
Digital Object Identifier: 10.3792/pjaa.98.013

Subjects:
Primary: 14H37
Secondary: 14H50

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

Rights: Copyright © 2022 The Japan Academy

Vol.98 • No. 8 • October 2022
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