The Maschke octic contains 96 pairwise disjoint lines

TL;DR

This paper confirms that the Maschke octic surface contains 96 disjoint lines, matching Miyaoka's theoretical maximum for degree 8 surfaces, thus establishing the bound's optimality.

Contribution

The paper verifies the maximum number of disjoint lines on the Maschke octic, confirming Miyaoka's bound is sharp for degree 8 surfaces.

Findings

Maschke octic contains 96 disjoint lines

Miyaoka's bound is proven to be optimal for d=8

Provides explicit geometric configuration of 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 $d=8$.