Automorphism group of plane curve computed by Galois points, II

2017/09/15 by Takeshi Harui, Harui, Takeshi, Kei Miura +3 · 2 citations
Engineering · Mathematics · #14H37 #14H50 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1709.05025

openalex publication_date 2017/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, the first author classified finite groups obtained as automorphism groups of smooth plane curves of degree d ≥ 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 \ 2 d (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 60 d. In fact, we determine the structure of the automorphism group of those curves.

Citations

• Automorphism groups of smooth plane curves

Cited by

• Subgroups of the Projective Linear Group Realized by wild Galois Points
• Persistence of Galois property of hypersurfaces over algebraic integers across other characteristics

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