Quasi-Galois points

TL;DR

This paper introduces the concept of quasi-Galois points in algebraic geometry, generalizing Galois points, and explores their properties, structures, and applications to automorphism groups of algebraic curves.

Contribution

It defines quasi-Galois points, analyzes their properties, and connects them to automorphism groups, extending the theory of Galois points in algebraic geometry.

Findings

Characterization of quasi-Galois points and their standard forms

Analysis of the Galois group structure for projections from quasi-Galois points

Applications to automorphism groups of algebraic curves

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 $\pi_P$ 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.