Ordres des courants positifs pluriharmoniques

TL;DR

This paper investigates the growth order of positive pluriharmonic currents, comparing it with slice and directional orders, and explores algebraicity conditions through growth estimates of the Lelong function.

Contribution

It introduces new comparisons between the order of pluriharmonic currents and their slices or directional orders, along with growth estimates of the Lelong function.

Findings

Established estimates for the growth of the Lelong function.

Compared the order of currents with slice and directional orders.

Addressed algebraicity conditions of currents.

Abstract

In this article, we study the order of a positive pluriharmonic current and we compare it with either the order of the concurrent slices or the directionnel orders of the current. Therefore some estimates of the growth of the \textsc{Lelong} function are established and the problem of algebraicity of the current is treated as a result.