Arakelov Geometry of Toric Bundles: Okounkov Bodies and BKK
Abstract
Abstract This article introduces the study of toric bundles and the morphisms between them from the perspective of adelic fibre bundles, as introduced by Chambert-Loir and Tschinkel. We study the Okounkov bodies and Boucksom–Chen transforms of suitable adelic line bundles on toric bundles. Finally, we prove an arithmetic analogue of a formula for intersection numbers due to Hofscheier, Khovanskii, and Monin. We apply this to the study of compactifications of semiabelian varieties, whose height and successive minima we compute. This extends computations of Chambert-Loir to arbitrary toric compactifications.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Geometry and complex manifolds
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 4
- Publication date
- 20 January 2026
- Language
- EN