Linear automorphisms of smooth hypersurfaces giving Galois points

Abstract

Let $X$ be a smooth hypersurface $X$ of degree $d\ge 4$ 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 function fields $\mathbb{C}(X)/\mathbb{C}({\mathbb{P}}^n)$. 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.

References in corpus (1)

• On Abelian Automorphism Groups of Hypersurfaces