Linear automorphisms of smooth hypersurfaces giving Galois points

Bull. Korean Math. Soc. Published online March 5, 2021

Taro Hayashi
Kindai University

Abstract : Let $X$ be a smooth hypersurface $X$ of degree $d\geq4$ in a projective space $\mathbb P^{n+1}$.
We consider a projection of $X$ from $p\in\mathbb P^{n+1}$ to a plane $H\cong\mathbb P^n$.
This projection induces an extension of fields $k(X)/k(\mathbb P^n)$.
The point $p$ is called a Galois point if the extension is Galois.
In this paper, we will give a necessary and sufficient conditions for $X$ to have Galois points by using linear automorphisms.

Keywords : Smooth hypersurface, Automorphism, Galois point, Galois extension