A bound for the number of lines lying on a nonsingular surface in $3$-space over a finite field

Masaaki Homma; Seon Jeong Kim

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arXiv · 1409.6421

A bound for the number of lines lying on a nonsingular surface in $3$-space over a finite field

Masaaki Homma·Seon Jeong Kim

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Abstract

A nonsingular surface of degree $d \geq 2$ in $\mathbb{P}^3$ over $\mathbb{F}_q$ has at most $((d-1)q+1)d$ $\mathbb{F}_q$-lines, and this bound is optimal for $d = 2, \sqrt{q}+1, q+1$.

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BibTeX RIS

Masaaki Homma, Seon Jeong Kim. 2014-09-23. A bound for the number of lines lying on a nonsingular surface in $3$-space over a finite field. https://arxiv.org/abs/1409.6421

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