Maximal Number of Skew Lines in the Fermat Surface

It is well-known that the Fermat surface of degree d≥ 3 has 3d² lines. However, it has not yet been established what is the maximum number of pairwise disjoint lines that it can have if d≥ 4. In this article we show that the maximal number of skew lines on the Fermat surface of degree d ≥ 4 is $3d$ either d even or d odd distinct of $5$, otherwise ($d = 5$) it contains no more than $13$ pairwise disjoint lines.