Transverse lines to surfaces over finite fields

Shamil Asgarli, Lian Duan, Kuan-Wen Lai

We prove that if $S$ is a smooth reflexive surface in ${\mathbb{P}}^3$ defined over a finite field ${\mathbb{F}}_q$, then there exists an ${\mathbb{F}}_q$-line meeting $S$ transversely p…