The Maschke octic contains 96 pairwise disjoint lines

Cédric Bonnafé

doi:10.56754/0719-0646.2803.449

Authors

Cédric Bonnafé IMAG, Université de Montpellier, CNRS, Montpellier, France

DOI:

https://doi.org/10.56754/0719-0646.2803.449

Keywords:

Lines in surfaces, skew lines, reflection groups

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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