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 \(d=8\).
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Finite Group Theory Research
Cryptography and Residue Arithmetic
Publication details
- Journal / source
- Cubo
- Volume
- 28
- Issue
- 3
- Pages
- 449–449
- Publication date
- 1 September 2026
- Language
- EN