Images Directes de Fibrés en Droites Adjoints

Abstract

Our main purpose is to study ampleness and positivity properties of the direct image $\phi \star L$ of a holomorphic line bundle $L$ under a smooth morphism $\phi :X\to Y$ between compact complex analytic manifolds. We show that in general the ampleness of $L$ does not imply that of the direct image $\phi \star L$ but only that of thé direct image of the adjoint line bundle $\phi \star (K_{X/Y}\otimes L)$.