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Singularité et intégrabilité des fonctions plurisousharmoniques

Mongi Blel; Saoud K. Mimouni — 2005

Annales de l’institut Fourier

On étudie les singularités et l’intégrabilité d’une classe de fonctions plurisousharmoniques sur une variété analytique $X$ de dimension $n \geq 1$ . Pour étudier ce problème, nous commençons par contrôler les nombres de Lelong de certains types de fonctions plurisousharmoniques $ϕ$ . Ensuite, nous étudions les singularités du transformé strict du courant $d d^{c} ϕ$ par un éclatement de $X$ au dessus d’un point. Nous répondons ainsi positivement au problème d’intégrabilité locale de $e^{- ϕ}$ , lorsque $\dim X = 2$ , et lorsque $ϕ$ est une fonction plurisousharmonique...

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