Classification of Du Val del Pezzo surfaces of Picard rank one in positive characteristic

Abstract

In this paper, we classify Du Val del Pezzo surfaces of Picard rank one in positive characteristic. We also show that if a Du Val del Pezzo surface is Frobenius split, then a general anti-canonical member is smooth. Furthermore, in characteristic two, it is an ordinary elliptic curve.Comment: 18 pages, this is an extended version of Sections 7 and 8 in arXiv:2008.07700v