The Maschke octic contains 96 pairwise disjoint lines
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918268481044480 |
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| author | Bonnafé, Cédric |
| author_facet | Bonnafé, Cédric |
| contents | 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 $d=8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Maschke octic contains 96 pairwise disjoint lines Bonnafé, Cédric Algebraic Geometry Representation Theory 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 $d=8$. |
| title | The Maschke octic contains 96 pairwise disjoint lines |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2601.00033 |