Galois Points for a Normal Hypersurface

We study Galois points for a hypersurface X with dimSing(X) ≤ dimX − 2. The purpose of this article is to determine the set ∆(X) of Galois points in characteristic zero: Indeed, we give a sharp upper bound of the number of Galois points in terms of dimX and dimSing(X) if ∆(X) is a finite set, and prove that X is a cone if ∆(X) is infinite. To achieve our purpose, we need a certain hyperplane section theorem on Galois point. We prove this theorem in arbitrary characteristic. On the other hand, the hyperplane section theorem has other important applications: For example, we can classify the Galois group induced from a Galois point in arbitrary characteristic and determine the distribution of Galois points for a Fermat hypersurface of degree pe + 1 in characteristic p > 0.