On Volumes of Arithmetic Line Bundles

Abstract

We show an arithmetic generalization of the recent work of Lazarsfeld-Mustata 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.

21 pages

References in corpus (1)

• Big Line Bundles over Arithmetic Varieties

Cited by in corpus (7)

• Okounkov bodies of filtered linear series
• Estimation of arithmetic linear series
• Big arithmetic divisors on the projective spaces over Z
• Effective bound of linear series on arithmetic surfaces
• Arakelov geometry, heights, equidistribution, and the Bogomolov conjecture
• Roth's Theorem over arithmetic function fields
• Adelic Cartier divisors with base conditions and the continuity of volumes