At most 64 lines on smooth quartic surfaces (characteristic 2)

TL;DR

This paper proves that smooth quartic surfaces over fields of characteristic 2 cannot have more than 64 lines, and constructs an example with 60 lines, setting a new record for such surfaces.

Contribution

It provides a geometric proof establishing the maximum number of lines on smooth quartic surfaces in characteristic 2 and presents an explicit example with 60 lines.

Findings

No smooth quartic has more than 64 lines in characteristic 2

Constructed a smooth quartic with 60 lines

Established a new record for lines on such surfaces

Abstract

Let K be a field of characteristic 2. We give a geometric proof that there are no smooth quartic surfaces in IP^3 with more than 64 lines (predating work of Degtyarev which improves this bound to 60). We also exhibit a smooth quartic containing 60 lines which thus attains the record in characteristic 2.