Locus of exceptional points and the multidirectional tangent cone of a closed positive current.

Let Omega be an open set in C-n, with n greater than or equal to 2 and let (X-k)(k) be a sequence of analytic sets of dimension p less than or equal t o n - 2 in Omega. We prove that there exists a positive (1, 1)-current T on Omega such that the tangent cone of T does not exist at any point of boole an ORk X-k. More precisely we prove that for every open set omega subset of Omega and for every analytic set of dimension p less than or equal to n - 2 in Omega, there exists a closed positive current T of bidegree (1, 1) on Omega such that the tangent cone of T does not exist on X boolean AND omega moreover we prove that for every closed positive current Theta of bidegree (1, 1), the tangent cone of the current T + Theta does not exist at any po int of X boolean AND omega. In the last paragraph, we study the directional and the multidirectional tangent cone associated to a closed positive curr ent. (C) 2000 Editions scientifiques et medicales Elsevier SAS.