Quasi-Galois points

2015/05/01 by Satoru Fukasawa, Fukasawa, Satoru, Kei Miura +3
Computer Science · Mathematics · #12F10 #14H05 #14H50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1505.00148

openalex publication_date 2015/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the new notion of the "quasi-Galois point" in Algebraic geometry, which is a generalization of the Galois point. A point P in projective plane is said to be quasi-Galois for a plane curve if the curve admits a non-trivial birational transformation which preserves the fibers of the projection π_P from P. We discuss the standard form of the defining equation of curves with quasi-Galois points, the number of quasi-Galois points, the structure of the Galois group for the projection, relations with dual curves, and so on. Our theory also has applications to the study of automorphism groups of algebraic curves.

Related

• Quasi-Galois points, II: Arrangements
• Algebraic curves admitting inner and outer Galois points
• Algebraic curves admitting non-collinear Galois points
• Bounds for the number of Galois points for plane curves
• Automorphism group of plane curve computed by Galois points, II