A criterion for the existence of a plane model with two inner Galois points for algebraic curves

TL;DR

This paper presents a generalized criterion for the existence of plane models with two non-smooth Galois points on algebraic curves, extending previous results for smooth Galois points and enabling detailed analysis of multiplicities and order sequences.

Contribution

It introduces a new criterion for non-smooth Galois points, broadening the understanding of algebraic curve models beyond smooth cases.

Findings

Generalized criterion for non-smooth Galois points

Detailed descriptions of multiplicities at Galois points

Enhanced understanding of order sequences at Galois points

Abstract

A criterion for the existence of a plane model with two non-smooth Galois points for algebraic curves is presented, which is a generalization of Fukasawa's criterion for two smooth Galois points. Owing to this generalized criterion, multiplicities and order sequences at Galois points can be described in detail.