Zariski K3 surfaces

In 1970’s Rudakov-Shafarevich showed that supersingular K3 surfaces in characteristic 2 are unirational and recently, Liedtke showed that supersingular K3 surfaces are unirational in characteristic p > 3. A surface X is said to be a Zariski surface if there exists a generically surjective rational map from the projective surface to X. By definition, a Zariski surface is unirational. In my talk, we give some results on the Zariskiness of algebraic surfaces, in particular, on the Zariskiness of supersingular K3 surfaces.