Maximal number of Skew lines on Fermat Surfaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917825107460096 |
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| author | Andria, Sally Rojas, Jacqueline Mangueira, Wállace |
| author_facet | Andria, Sally Rojas, Jacqueline Mangueira, Wállace |
| contents | It is well-known that the Fermat surface of degree $d\geq 3$ has $3d^2$ lines. However, it has not yet been established what is the maximal number of pairwise disjoint lines that it can have if $d\geq 4$. In this article we show that the maximal number of skew lines on the Fermat surface of degree $d\geq 4$ is $3d$, either $d$ even or $d$ odd distinct of 5, otherwise ($d=5$) it contains no more than 13 pairwise disjoint lines. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_15666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal number of Skew lines on Fermat Surfaces Andria, Sally Rojas, Jacqueline Mangueira, Wállace Algebraic Geometry Commutative Algebra Number Theory 14N10, 14N20, 11A07 It is well-known that the Fermat surface of degree $d\geq 3$ has $3d^2$ lines. However, it has not yet been established what is the maximal number of pairwise disjoint lines that it can have if $d\geq 4$. In this article we show that the maximal number of skew lines on the Fermat surface of degree $d\geq 4$ is $3d$, either $d$ even or $d$ odd distinct of 5, otherwise ($d=5$) it contains no more than 13 pairwise disjoint lines. |
| title | Maximal number of Skew lines on Fermat Surfaces |
| topic | Algebraic Geometry Commutative Algebra Number Theory 14N10, 14N20, 11A07 |
| url | https://arxiv.org/abs/2403.15666 |