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arXiv · 2403.15666

Maximal number of Skew lines on Fermat Surfaces

Sally Andria·Jacqueline Rojas·Wállace Mangueira
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Abstract

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.

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Sally Andria, Jacqueline Rojas, Wállace Mangueira. 2024-03-23. Maximal number of Skew lines on Fermat Surfaces. https://arxiv.org/abs/2403.15666

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