Singularities of normal quartic surfaces II (char=2)

Abstract

We show, in this second part, that the maximal number of singular points of a quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic 2 is at most 14, and that, if we have 14 singularities, these are nodes and moreover the minimal resolution of $X$ is a supersingular K3 surface. We produce an irreducible component, of dimension 24, of the variety of quartics with 14 nodes. We also exhibit easy examples of quartics with 7 $A_3$-singularities.