The maximal number of skew lines on Schur’s quartic

Abstract

Since 1882 it is known that the so-called Schur’s quartic contains exactly 64 lines.However, it has not yet been establishedwhat is themaximumnumber of pairwise disjoint lines that it can have. The aim of our work is to show in an elementary and self-contained way that the maximum number of pairwise disjoint lines in Schur’s quartic is 16 (without using Nikulins’s theorem or Miyaoka’s upper bound).