Bulletin of the
Korean Mathematical Society BKMS

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 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 necessary and sufficient conditions for $X$ to have Galois points by using linear automorphisms.

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

MSC numbers: Primary 14J70; Secondary 12F10