Classification of Du Val del Pezzo surfaces of Picard rank one in characteristic two and three

Abstract

In this paper, we classify Du Val del Pezzo surfaces of Picard rank one in characteristic two and three. 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.

21 pages, final version, to appear in Journal of Algebra. arXiv admin note: substantial text overlap with arXiv:2008.07700