Monge–Ampère measures for toric metrics on abelian varieties
Publications mathématiques de Besançon. Algèbre et théorie des nombres (2023), pp. 49-84.

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.

Les métriques toriques sur un fibré en droites sur une variété abélienne A sont les métriques invariantes sous l’action naturelle du tore issue de la théorie de l’uniformisation de Raynaud. Nous calculons les mesures de Monge–Ampère associées pour les restrictions à toutes les sous-variétés fermées de A. Ceci généralise des travaux du premier auteur sur le calcul des mesures canoniques pour des valuations discrètes au cas des métriques toriques pour des corps non archimédiens arbitraires.

Published online:
DOI: 10.5802/pmb.49
Classification: 14G40, 11G10, 14G22
Keywords: Berkovich analytic spaces, formal geometry, abelian varieties, canonical measures

Walter Gubler 1; Stefan Stadlöder 1

1 Mathematik, Universität Regensburg, 93040 Regensburg, Germany
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Walter Gubler; Stefan Stadlöder. Monge–Ampère measures for toric metrics on abelian varieties. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2023), pp. 49-84. doi : 10.5802/pmb.49. https://pmb.centre-mersenne.org/articles/10.5802/pmb.49/

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