Higher dimensional essential minima and equidistribution of cycles
Annales de l'Institut Fourier, Volume 72 (2022) no. 4, pp. 1329-1377.

The essential minimum and equidistribution of small points are two well-established interrelated subjects in arithmetic geometry. However, there is lack of an analogue of essential minimum dealing with higher dimensional subvarieties, and the equidistribution of these is a far less explored topic.

In this paper, we introduce a new notion of higher dimensional essential minimum and use it to prove equidistribution of generic and small effective cycles. The latter generalizes the previous higher dimensional equidistribution theorems by considering cycles and by allowing more flexibility on the arithmetic datum.

Le minimum essentiel et l’équirépartition des petits points sont deux sujets entrelacés et bien établis en géométrie arithmétique. Cependant, on manque d’un analogue pour le minimum essentiel pour des sous-variétés de dimension supérieure, et l’équirépartition de celles-ci est un sujet beaucoup moins exploré.

Dans cet article, on introduit une nouvelle notion de minimum essentiel de dimension supérieure et on l’utilise pour prouver un résultat d’équirépartition pour des cycles effectifs. Celui-ci généralise les théorèmes d’équirépartition de dimension supérieure précédents en permettant plus de flexibilité sur les données arithmétiques.

Received:
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Accepted:
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DOI: 10.5802/aif.3500
Classification: 14G40, 11G35, 14C25
Keywords: Equidistribution of cycles, Arakelov geometry, Heights, Essential minimum
Mot clés : Équirépartition de cycles, Géométrie d’Arakelov, Hauteurs, Minimum essentiel

Gualdi, Roberto 1; Martínez, César 1

1 Fakultät für 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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Gualdi, Roberto; Martínez, César. Higher dimensional essential minima and equidistribution of cycles. Annales de l'Institut Fourier, Volume 72 (2022) no. 4, pp. 1329-1377. doi : 10.5802/aif.3500. https://aif.centre-mersenne.org/articles/10.5802/aif.3500/

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