Log del Pezzo surfaces with not small fractional indices

preprint2014arXivOpen access

Abstract

For a log del Pezzo surface SS, the fractional index r(S)∈Q>0r(S)\in\mathbb{Q}_{>0} is the maximum of rr with which −KS-K_S can be written as rr times some Cartier divisor. We classify all the log del Pezzo surfaces SS with r(S)≥1/2r(S)\geq 1/2, after the technique of Nakayama.

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