Examples of plane rational curves with two Galois points in positive characteristic, II

2021/03/03 by Satoru Fukasawa, Fukasawa, Satoru, Katsushi Waki +1
Computer Science · Mathematics · #14H50 #20G40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2103.02218

openalex publication_date 2021/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that there exist plane rational curves of degree twelve (resp. twenty-four) with two different outer Galois points such that the Galois group at one of two Galois points is an alternating group A₄ (resp. a symmetric group S₄) of degree four, under the assumption that the characteristic of the ground field is eleven (resp. is twenty-three). For an alternating group A₅ of degree five, a similar existence theorem is confirmed, over a field of characteristic 59, by GAP system.

Related

• Plane curves possessing two outer Galois points
• Rational curves of degree four with two inner Galois points
• Curves with more than one inner Galois point
• Algebraic curves admitting inner and outer Galois points
• Automorphism group of plane curve computed by Galois points, II