-estimates and existence theorems for generalized analytic functions in several variables.
Soit un fibré holomorphe localement trivial de base une variété de Stein et de fibre une courbe compacte.Si est un ouvert localement pseudoconvexe de ne contenant aucune fibre, alors est de Stein.
We generalize a theorem of Siciak on the polynomial approximation of the Lelong class to the setting of toric manifolds with an ample line bundle. We also characterize Lelong classes by means of a growth condition on toric manifolds with an ample line bundle and construct an example of a nonample line bundle for which Siciak's theorem does not hold.
Define a line bundle on a projective variety to be -ample, for a natural number , if tensoring with high powers of kills coherent sheaf cohomology above dimension . Thus 0-ampleness is the usual notion of ampleness. We show that -ampleness of a line bundle on a projective variety in characteristic zero is equivalent to the vanishing of an explicit finite list of cohomology groups. It follows that -ampleness is a Zariski open condition, which is not clear from the definition.