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Log canonical thresholds of del Pezzo surfaces in characteristic p

Martinez-Garcia, Jesus (2014) 'Log canonical thresholds of del Pezzo surfaces in characteristic p.' Manuscripta Mathematica, 145 (1-2). 89 - 110. ISSN 0025-2611

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Abstract

The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Kollár–Shokurov’s connectedness principle and other results relying on vanishing theorems of Kodaira type, not known to be true in finite characteristic. We compute the global log canonical threshold of non-singular del Pezzo surfaces over an algebraically closed field. We give algebraic proofs of results previously known only in characteristic 0. Instead of using of the connectedness principle we introduce a new technique based on a classification of curves of low degree. As an application we conclude that non-singular del Pezzo surfaces in finite characteristic of degree lower or equal than 4 are K-semistable.

Item Type: Article
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 30 Aug 2019 15:31
Last Modified: 30 Aug 2019 16:15
URI: http://repository.essex.ac.uk/id/eprint/25200

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