Unirationality of del Pezzo surfaces of degree $2$ over finite fields

A variety $X$ over a field $k$ is unirational if there is a dominant map $\mathbb{P}^m\dashrightarrow X$ defined over $k$. Work of Segre, Manin and Kollár shows that del Pezzo surfaces of degree $d>2$ over any field $k$ are unirational, provided $X(k)$ is non-empty. Following C. Salgado, D. Testa, and A. Várilly-Alvarado, we will discuss theorem on the unirationality of del Pezzo surfaces of degree $2$ over finite fields.