Characterization of log del Pezzo pairs via anticanonical models

Abstract

We give a characterization of log del Pezzo pairs in terms of their anticanonical models. As a first application, we show that every non-rational del Pezzo surface with log canonical singularities is of Picard number one and contains a unique singularity which is simple elliptic. As a second application, we verify a conjecture of Smith and Schwede in dimension two which says that every surface of globally F-regular type is of Fano type.