Almost All Transverse-Free Plane Curves Are Trivially Transverse-Free

Alejandro Lopez, Bella Villarreal, Ren Watson +1

We call a curve $C\subset {\mathbb{P}}^2$ defined over ${\mathbb{F}}_q$ \textit{transverse-free} if for every line, $\ell$, over ${\mathbb{F}}_q$, $C\cap \ell$ is not a smooth dimensio…