LIMITS OF MULTIPOLE PLURICOMPLEX GREEN FUNCTIONS

作者：Magnusson Jon I^*; Rashkovskii Alexander; Sigurdsson Ragnar; Thomas Pascal J

来源：International Journal of Mathematics, 2012, 23(6): 1250065.

DOI：10.1142/S0129167X12500656

• Pluricomplex Green function
• complex Monge-Ampere equation
• residues
• analytic disks
• ideals of holomorphic functions
• Hilbert-Samuel multiplicity
• Briancon-Skoda theorem

Let Omega be a bounded hyperconvex domain in C-n, 0 is an element of Omega, and S-epsilon a family of N poles in Omega, all tending to 0 as epsilon tends to 0. To each S-epsilon we associate its vanishing ideal I-epsilon and pluricomplex Green function G(epsilon) = G(I epsilon). %26lt;br%26gt;Suppose that, as epsilon tends to 0, (I-epsilon)(epsilon) converges to I (local uniform convergence), and that (G(epsilon))(epsilon) converges to G, locally uniformly away from 0; then G %26gt;= G(I). If the Hilbert-Samuel multiplicity of I is strictly larger than its length (codimension, equal to N here), then (G(epsilon))(epsilon) cannot converge to G(I). Conversely, if I is a complete intersection ideal, then (G(epsilon))(epsilon) converges to G(I). We work out the case of three poles.

• 出版日期2012-6