Limits of multipole pluricomplex green functions

Let Ω be a bounded hyperconvex domain in &Cmathbb; ⁿ, 0 ∈ Ω, and S _ε a family of N poles in Ω, all tending to 0 as ε tends to 0. To each S _ε we associate its vanishing ideal Iε and pluricomplex Green function G _ε = GI _ε. Suppose that, as ε tends to 0, (I _ε) converges to I (local uniform convergence), and that (G _ε) _ε converges to G, locally uniformly away from 0; then G ≥ G _I. If the HilbertSamuel multiplicity of I is strictly larger than its length (codimension, equal to N here), then (G _ε) _ε cannot converge to G _I. Conversely, if I is a complete intersection ideal, then (G _ε) _ε converges to G _I. We work out the case of three poles.