具有外伽罗瓦点的光滑平面曲线,其约简自同构群为$A_{5}$

Pub Date : 2022-10-11 DOI:10.3792/pjaa.98.013
Takeshi Harui, Kei Miura, A. Ohbuchi
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引用次数: 0

摘要

在[8]中,作者将不小于4次光滑平面曲线的自同构群划分为5类。如果曲线有唯一的外伽罗瓦点,则其自同构群与该点处的伽罗瓦群的商群称为约化自同构群,是一维射影线性群的有限子群。本文是[10]和[9]的续集。本文给出了约化自同构群为二十面体群时曲线的定义方程,并给出了满自同构群的描述。
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Smooth plane curves with outer Galois points whose reduced automorphism group is $A_{5}$
: 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.
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