A calculus for meromorphic currents.
A version of the classical Nakai-Moishezon criterion is proved for all compact complex surfaces, regardless of the parity of the first Betti number.
We provide a new division formula for holomorphic mappings. It is given in terms of residue currents and has the advantage of being more explicit and simpler to prove than the previously known formulas.
We investigate ramification properties with respect to parameters of integrals (distributions) of a class of singular functions over an unbounded cycle which may intersect the singularities of the integrand. We generalize the classical result of Nilsson dealing with the case where the cycle is bounded and contained in the set of holomorphy of the integrand. Such problems arise naturally in the study of exponential representation at infinity of solutions to certain PDE's (see [Z]).
We consider a nondegenerate holomorphic map where is a compact Hermitian manifold of dimension larger than or equal to and is an open connected complex manifold of dimension . In this article we give criteria which permit to construct Ahlfors’ currents in .
Dans cet article, nous étudions les zéros des fonctions holomorphes dans le bidisque dont le logarithme du module vérifie une condition de croissance : nous caractérisons par une condition de type Blaschke les zéros des fonctions vérifiantpour , et nous donnons les conditions suffisantes pour des classes plus petites, en particulier pour la classe de Nevanlinna du bidisque.