2003/06/05 by Tien‐Cuong Dinh, T. C. Dinh, Nessim Sibony +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.DS
paper · pdf · doi:10.48550/arxiv.math/0306095
56 pages, in French
arxiv created 2003/06/05 · openalex publication_date 2003/06/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A meromorphic transform between complex manifolds is a surjective mutivalued map with an analytic graph. Let Fn be a sequence of meromorphic transforms from a compact Kahler manifold X into compact Kahler manifolds Xn. We give conditions which imply that the behavior of the sequence of preimages Fn-1(xn) of xn does not depend on the generic sequence of points (x1,x2,....). Using this formalism, we obtain sharp results on the limit distribution of common zeros, of l random holomorphic sections of high powers Ln of a positive holomorphic line bundle L over a projective manifold X. We consider also the equidistribution problem for random iteration of correspondences. If f is a meromorphic self correspondence of a compact Kahler manifold X, under a hypothesis on the dynamical degrees, we construct an f^*-invariant probability measure μ such that quasi-p.s.h. functions are μ-integrable. Every projective manifold admits such correspondences. When f is a meromorphic map, the measure μ is exponentially mixing. We give some analogous results for random iterations of correspondences. We also consider the problem of equidistribution of preimages of subvarieties for a correspondences and more precisely for polynomial automorphisms.