UC San Diego

A log del Pezzo surface is a klt projective surface whose canonical divisor is anti-ample. We classify all log del Pezzo surfaces of Picard number one defined over algebraically closed fields of characteristic different from two and three. We also discuss some consequences of the classification. For example, we show that log del Pezzo surfaces defined over algebraically closed fields of characteristic higher than five have at most four singular points and admit a log resolution that lifts to characteristic zero over a smooth base.