Limit currents and value distribution of holomorphic maps

[Courants limites et distribution de valeurs des applications holomorphes]

Burns, Daniel ; Sibony, Nessim

Annales de l'Institut Fourier, Tome 62 (2012), p. 145-176 / Harvested from Numdam

Résumé

Nous introduisons des courants positifs $d$-fermés ou $dd^c$-fermés associés à une application holomorphe $\phi $ entre deux variétés complexes. Les courants sont de bidegré $(p,p)$ selon les indicateurs de croissance de $\phi $. Ce sont les analogues des courants d’Ahfors associés aux applications de $\mathbb{C}$ dans une variété $Y$. Nous donnons quelques applications à la théorie de distribution de valeurs.

Abstract

We construct $d$-closed and $dd^c$-closed positive currents associated to a holomorphic map $\phi $ via cluster points of normalized weighted truncated image currents. They are constructed using analogues of the Ahlfors length-area inequality in higher dimensions. Such classes of currents are also referred to as Ahlfors currents. We give some applications to equidistribution problems in value distribution theory.

Détail

Publié le : 2012-01-01

MR 2986269 | Zbl 1252.32002

DOI : https://doi.org/10.5802/aif.2703
Classification:  32A22,  32H25,  32H30
Mots clés: Courants d’Ahlfors, théorème de Brody, théorie de la distribution de valeurs, équidistribution

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