The Maschke octic contains 96 pairwise disjoint lines

Abstract

Miyaoka proved that a smooth surface of degree $d$ in ${\mathbf{P}}^3(\mathbb{C})$ contains at most $2d(d-2)$ pairwise disjoint lines. In this note, we verify that the Maschke octic contains $96$ pairwise disjoint lines, thereby proving that Miyaoka's bound is optimal for $d=8$.

3 pages