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The Maschke octic contains 96 pairwise disjoint lines
Published 30 Dec 2025 in math.AG and math.RT | (2601.00033v1)
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 $d=8$.
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