Monge–Ampère measures for toric metrics on abelian varieties

Walter Gubler; Stefan Stadlöder

doi:10.5802/pmb.49

Monge–Ampère measures for toric metrics on abelian varieties
[Mesures de Monge-Ampère pour les métriques toriques sur les variétés abéliennes]

Walter Gubler ¹ ; Stefan Stadlöder ¹

¹ Mathematik, Universität Regensburg, 93040 Regensburg, Germany

Publications mathématiques de Besançon. Algèbre et théorie des nombres (2023), pp. 49-84.

Résumé
Abstract

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.

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.

Publié le : 2023-06-15

DOI : 10.5802/pmb.49

Classification : 14G40, 11G10, 14G22
Mots clés : Berkovich analytic spaces, formal geometry, abelian varieties, canonical measures

Affiliations des auteurs :

Walter Gubler ¹ ; Stefan Stadlöder ¹

¹ Mathematik, Universität Regensburg, 93040 Regensburg, Germany

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Monge{\textendash}Amp\`ere measures for toric metrics on abelian varieties},
     journal = {Publications math\'ematiques de Besan\c{c}on. Alg\`ebre et th\'eorie des nombres},
     pages = {49--84},
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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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