Compositio Mathematica

Table of Contents - 2009 - Volume 145, Issue 06  

Research Article

On volumes of arithmetic line bundles

Xinyi Yuana1

a1 School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA (email: yxy@ias.edu)

Abstract

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.

(Received November 12 2008)

(Accepted March 05 2009)

2000 Mathematics Subject Classification

  • 14G40 (primary);
  • 11G35;
  • 11G50 (secondary)

Keywords

  • arithmetic varieties;
  • Hermitian line bundles;
  • Arakelov theory;
  • volumes of line bundles;
  • big line bundles;
  • Fujita approximation;
  • Hodge index theorem

Footnotes

The author is fully supported by a research fellowship of the Clay Mathematics Institute.