On the proof of castelnuovo's rationality criterion in positive characteristic

Abstract

One of the final step 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.