On singularity types of del Pezzo surfaces with rational double points in positive characteristic

Tatsuro Kawakami, Masaru Nagaoka

Published 2020-06-08Version 1

In this paper, we prove that a pair of the minimal resolution of a del Pezzo surface with rational double points whose general anti-canonical member is smooth and its exceptional divisor lifts to the Witt ring. We also classify a del Pezzo surface with rational double points whose anti-canonical members are all singular. As a corollary, we determine all singularity types of del Pezzo surfaces with rational double points which only appear in positive characteristic.