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タイトル: Classification of log del~Pezzo surfaces of index two
著者: Nakayama, Noboru
キーワード: del Pezzo surface
ruled surface
extremal ray
発行日: 2007年10月15日
出版者: Graduate School of Mathematical Sciences, The University of Tokyo
掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 14 (2007), No. 3, Page 293-498
抄録: In this article, a log del~Pezzo surface of index two means a projective normal non-Gorenstein surface \( S \) such that \( (S, 0) \) is a log-terminal pair, the anti-canonical divisor \( -K_{S} \) is ample and that \( 2K_{S} \) is Cartier. The log del~Pezzo surfaces of index two are shown to be constructed from data \( (X, E, \Delta) \) called fundamental triplets consisting of a non-singular rational surface \( X \), a simple normal crossing divisor \( E \) of \( X \), and an effective Cartier divisor \( \Delta \) of \( E \) satisfying a suitable condition. A geometric classification of the fundamental triplets gives a classification of the log del~Pezzo surfaces of index two. As a result, any log del~Pezzo surface of index two can be described explicitly as a subvariety of a weighted projective space or of the product of two weighted projective spaces. This classification does not use the theory of K3 lattices, which is essential for the classification by Alexeev--Nikulin \cite{AN}. The comparison between two classifications is also discussed.
URI: http://hdl.handle.net/2261/20685
ISSN: 13405705
出現カテゴリ:Journal of Mathematical Sciences, the University of Tokyo
Journal of Mathematical Sciences, the University of Tokyo

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