On the proof of Castelnuovo's rationality criterion in positive characteristic (Q1173725)

One of the final steps in Zariski's proof of Castelnuovo's rationality criterion is to show the existence of `lines' on a Del Pezzo surface. Here, looking at the anticanonical model, we find the number of exceptional curves of the first kind, and their incidence configuration, on a smooth Del Pezzo surface with \(K^ 2=2\) over an algebraically closed field of characteristic 2, using computational techniques.