Quartic K3 surfaces without nontrivial automorphisms

Abstract

For any field k we fix an algebraic closure of k, denoted by k. For a variety X ⊂ P k we set X = X×k k, we say that X is smooth if X is regular, and we let AutX denote the group of k-automorphisms of X, while LinX denotes the group of linear automorphisms of X, i.e., automorphisms induced by a linear transformation of the coordinates of P. The following theorem was proved by Poonen, see [Po], Thm. 1.6.