Images Directes de Fibres en Droites Adjoints

Abstract

Our main purpose is to study ampleness and positivity properties of the direct image φ ⋆_L_ of a holomorphic line bundle L under a smooth morphism φ: X → Y between compact complex analytic manifolds. We show that in general the ampleness of L does not imply that of the direct image φ ⋆_L_ but only that of thé direct image of the adjoint line bundle (φ ⋆(KX/Y/i> ⊗_L)._