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

Abstract

A nonsingular surface of degree $d\ge 2$ 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 $d=2,\sqrt{q}+1,q+1$.

4 pages. An incorrect argument was fixed

Cited by in corpus (1)

• 112 lines on smooth quartic surfaces (characteristic 3)