Unirationality of del Pezzo surfaces of degree 2 over finite fields

festi, dino; van luijk, ronald;

We prove that every del Pezzo surface of degree 2 over a finite field is unirational, building on the work of Manin and an extension by Salgado, Testa, and V´arilly-Alvarado, who had proved this for all but three surfaces. Over general fields of characteristic not equal to 2, we state sufficient conditions for a del Pezzo surface of degree 2 to be unirational.