Characterization of Non-F-split del Pezzo Surfaces of Degree 2

We investigate a smooth del Pezzo surface of degree 2 which is not Frobenius split. We give a characterization of non-F-split del Pezzo surfaces of degree 2 which exist only if the characteristic of the ground field is 2 or 3. Moreover, we prove that the set of centers of the blow-ups on P-2 which gives a non-F-split del Pezzo surface is projectively equivalent to the only complete 7-arc over F-9 if the characteristic is 3.