Smooth Surfaces with Maximal Lines
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914847852068864 |
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| author | Page, Janet Ryan, Tim Smith, Karen E. |
| author_facet | Page, Janet Ryan, Tim Smith, Karen E. |
| contents | We prove that a smooth projective surface of degree $d$ in $\mathbb P^3$ contains at most $d^2(d^2-3d+3)$ lines. We characterize the surfaces containing exactly $d^2(d^2-3d+3)$ lines: these occur only in prime characterize $p$ and, up to choice of projective coordinates, are cut out by equations of the form $x^{p^{e}+1}+y^{p^{e}+1}+z^{p^{e}+1}+ w^{p^{e}+1} = 0.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15868 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smooth Surfaces with Maximal Lines Page, Janet Ryan, Tim Smith, Karen E. Algebraic Geometry Commutative Algebra primary: 14N10, secondary: 13A35, 51E12, 14J25, 14N15, 14G17 We prove that a smooth projective surface of degree $d$ in $\mathbb P^3$ contains at most $d^2(d^2-3d+3)$ lines. We characterize the surfaces containing exactly $d^2(d^2-3d+3)$ lines: these occur only in prime characterize $p$ and, up to choice of projective coordinates, are cut out by equations of the form $x^{p^{e}+1}+y^{p^{e}+1}+z^{p^{e}+1}+ w^{p^{e}+1} = 0.$ |
| title | Smooth Surfaces with Maximal Lines |
| topic | Algebraic Geometry Commutative Algebra primary: 14N10, secondary: 13A35, 51E12, 14J25, 14N15, 14G17 |
| url | https://arxiv.org/abs/2406.15868 |