Abstract
The goal of the present work is to study the singularities of a class of plurisubharmonic functions on complex manifolds X of dimension n >= 1. In order to study this problem one starts by controlling the Lelong numbers of certain of plurisubharmonic functions phi. Then we study the singularities of the strict transform of the current dd(c)phi by the blow-ups of X at a point. Using this we positively answer the question of the local integrability of e(-phi), when dimX = 2 and phi is a plurisubharmonic function with phi is an element of L-loc(infinity) (X/K), and K is a compact of X, and the situation where the sublevel sets E-c(phi) = {x is an element of X; v(phi)(x) >= c} is discrete for all c > 0 and v(phi)(x) <= 2 for all x is an element of X.