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

Masaaki Homma; Seon Jeong Kim

arxiv: 1409.6421 · v2 · pith:V337S22Pnew · submitted 2014-09-23 · 🧮 math.AG

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

Masaaki Homma , Seon Jeong Kim This is my paper

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keywords mathbbboundlinesnonsingularsurfacedegreefieldfinite

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

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