A hyperplane section theorem for Galois points and its application

TL;DR

This paper establishes a hyperplane section theorem for Galois points on hypersurfaces, showing that Galois properties are preserved under general hyperplane sections, and applies this to classify hypersurfaces with large sets of Galois points.

Contribution

It introduces a hyperplane section theorem for Galois points and applies it to classify hypersurfaces with extensive Galois point sets.

Findings

Galois points are preserved under general hyperplane sections.

Classification of hypersurfaces with n-dimensional sets of Galois points.

Extension of Galois point theory to higher-dimensional hypersurfaces.

Abstract

A point $P$ in projective space is said to be Galois with respect to a hypersurface if the function field extension induced by the projection from $P$ is Galois. We present a hyperplane section theorem for Galois points. Precisely, if $P$ is a Galois point for a hypersurface, then $P$ is Galois for a general hyperplane section passing through $P$. As an application, we determine hypersurfaces of dimension $n$ with $n$-dimensional sets of Galois points.