Monge-Ampère measures for toric metrics on abelian varieties

Abstract

Toric metrics on a line bundle of an abelian variety $A$ are the invariant metrics under the natural torus action coming from Raynaud's uniformization theory. We compute here the associated Monge-Ampère measures for the restriction to any closed subvariety of $A$. This generalizes the computation of canonical measures done by the first author from canonical metrics to toric metrics and from discrete valuations to arbitrary non-archimedean fields.

arXiv comment28 pages. Presentation in Section 3 changed to make the arguments easier to follow

References in corpus (10)

• Big Line Bundles over Arithmetic Varieties
• The Bogomolov conjecture for totally degenerate abelian varieties
• Tropical varieties for non-archimedean analytic spaces
• Mesures et équidistribution sur les espaces de Berkovich
• Non-archimedean canonical measures on abelian varieties
• A tropical approach to non-archimedean Arakelov theory
• Non-Archimedean and tropical theta functions
• Log smoothness and polystability over valuation rings
• Geometric Bogomolov conjecture in arbitrary characteristics
• Heights in families of abelian varieties and the Geometric Bogomolov Conjecture