Sequences of multivalued meromorphic maps and laminar currents

Abstract

Let (F_n) be a sequence of (multivalued) meromorphic maps between compact Kaehler manifolds X1 and X2. We study the asymptotic distribution of preimages of points by F_n and the asymptotic distribution of fixed points for multivalued self-maps of a compact Riemann surface. Let (Z_n) be a sequence of holomorphic images of the projective space P^s in a projective manifold. We prove that the currents, defined by integration on Z_n, properly normalized, converge to weakly laminar currents. We also show that the Green currents, of suitable bidimensions, associated to a regular polynomial automorphism, are (weakly) laminar.