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On volumes of arithmetic line bundles

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry

Published online by Cambridge University Press:  03 December 2009

Xinyi Yuan
Xinyi Yuan*
Affiliation:
School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA (email: yxy@ias.edu)
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Abstract

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We show an arithmetic generalization of the recent work of Lazarsfeld–Mustaţǎ which uses Okounkov bodies to study linear series of line bundles. As applications, we derive a log-concavity inequality on volumes of arithmetic line bundles and an arithmetic Fujita approximation theorem for big line bundles.

Keywords

arithmetic varietiesHermitian line bundlesArakelov theoryvolumes of line bundlesbig line bundlesFujita approximationHodge index theorem

MSC classification

Secondary: 14G40: Arithmetic varieties and schemes; Arakelov theory; heights 11G35: Varieties over global fields 11G50: Heights
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 6 , November 2009 , pp. 1447 - 1464
Copyright
Copyright © Foundation Compositio Mathematica 2009

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