Singularities of normal quartic surfaces III (char=2, non-supersingular)

TL;DR

This paper establishes an upper bound of 12 singular points for certain normal quartic surfaces in characteristic 2 and provides explicit examples, advancing understanding of surface singularities in algebraic geometry.

Contribution

It proves a maximum singularity count for non-supersingular quartic surfaces in characteristic 2 and constructs explicit examples in any characteristic.

Findings

Maximum of 12 singular points for the specified surfaces

Explicit examples of such surfaces in any characteristic

Clarification of singularity limits in characteristic 2

Abstract

We show that the maximal number of singular points of a normal quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic 2 is at most 12, if the minimal resolution of $X$ is not a supersingular K3 surface. We also provide a family of explicit examples, valid in any characteristic.