Lines on K3 quartic surfaces in characteristic 2

TL;DR

This paper establishes an upper bound of 68 lines on K3 quartic surfaces over fields of characteristic 2 and characterizes the unique family attaining this maximum.

Contribution

It proves the maximum number of lines on such surfaces and identifies the specific family of surfaces that achieve this maximum.

Findings

Maximum of 68 lines on K3 quartic surfaces in characteristic 2

Characterization of the unique family with 68 lines

Connection to previously known family by Rams and Schütt

Abstract

We prove that a K3 quartic surface defined over a field of characteristic 2 can contain at most 68 lines. If it contains 68 lines, then it is projectively equivalent to a member of a 1-dimensional family found by Rams and Sch\"utt.