Descendants of algebraic curves admitting two Galois points

2023/06/28 by Fukasawa, Satoru
#14H05 #14H37 #14H50 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.16044

Abstract

A connection between Galois points of an algebraic curve and those of a quotient curve is presented; in particular, the notion of a descendant of algebraic curves admitting two Galois points is introduced. It is shown that all descendants of a Fermat curve are Fermat curves; in particular, a Fermat curve does not have a descendant if and only if the degree is a prime.

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• Algebraic curves admitting non-collinear Galois points
• On the number of Galois points for a plane curve in characteristic zero
• Quasi-Galois points
• Bounds for the number of Galois points for plane curves
• Simultaneous Galois points for a reducible plane curve consisting of nonsingular components