Characterization of log del Pezzo pairs via anticanonical models
type: Item
instance of: scholarly article
title: Characterization of log del Pezzo pairs via anticanonical models
zbMATH Open document ID: 1332.14048
author: Jinhyung Park
author: Dongseon Hwang
published in: Mathematische Zeitschrift
publication date: 2015-06-18T00:00:00Z
full work available at URL: https://arxiv.org/abs/1303.2973
review text: 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}].
reviewed by: Linquan Ma
Mathematics Subject Classification ID: 14J45
Mathematics Subject Classification ID: 14J26
Mathematics Subject Classification ID: 13A35
Mathematics Subject Classification ID: 14J17
zbMATH DE Number: 6446931
zbMATH Keywords: log del Pezzo pair
zbMATH Keywords: big anticanonical surface
zbMATH Keywords: anticanonical model
zbMATH Keywords: globally F-regular variety
MaRDI profile type: Publication
OpenAlex ID: W2083138382
arXiv ID: 1303.2973
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DOI: 10.1007/S00209-015-1419-6
description: scientific article