A note on Galois embedding and its application to $\mathbb P^n$

Abstract

We show a condition that a Galois covering $\pi : V \longrightarrow \mathbb P^n$ is induced by a Galois embedding. Then we consider the Galois embedding for $\mathbb P^n$. If the Galois group $G$ is abelian, then $G \cong \bigoplus\limits^{n} Z_d$ and the projection $\pi$ can be expressed as $\pi(X_0:X_1: \cdots :X_n)=({X_0}^d:{X_1}^d:\cdots:{X_n}^d)$.