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arXiv · 2601.00033

The Maschke octic contains 96 pairwise disjoint lines

Cédric Bonnafé
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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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Cédric Bonnafé. 2025-12-30. The Maschke octic contains 96 pairwise disjoint lines. https://arxiv.org/abs/2601.00033

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