Images directes de fibrés en droites adjoints

Abstract

Our main purpose is to study ampleness and positivity properties of the direct image φ(Black star sign)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(Black star sign)L but only that of the direct image of the adjoint line bundle φ(Black star sign)(KX/Y⊗L).