Characterization of log del Pezzo pairs via anticanonical models
In this paper, the authors prove the following result: Let \(X\) be a smooth projective surface, then \((X,\Delta)\) is a klt (resp. weak lc) del Pezzo pair for some effective Q-divisor \(\Delta\) on X if and only if the anticanonical model of \(X\) is a klt (resp. lc) del Pezzo surface. The authors give several applications of this result. For example, they show that every non-rational del Pezzo surface with log canonical singularities is of Picard number one and contains exactly one simple elliptic singulairy. Another application is that surfaces of globally \(F\)-regular type is of log Fano type, which gives an answer to a question \textit{K. Schwede} and \textit{K. E. Smith} [Adv. Math. 224, No. 3, 863--894 (2010; Zbl 1193.13004)] in the surface case. This last result is also obtained independently by \textit{S. Okawa} [``Surfaces of globally \(F\)-regular type are of Fano type'', preprint, \url{arXiv:1506.04900}], and by \textit{Y. Gongyo} and \textit{S. Takagi} [``Surfaces of globally \(F\)-regular and \(F\)-split type'', preprint, \url{arXiv: 1305.3056}].
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