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Direct images of adjoint line bundles. (Images directes de fibrés en droites adjoints.) (French) Zbl 0926.14004
The author studies ampleness and positivity properties of the direct image $$\varphi_*L$$ of a holomorphic line bundle $$L$$ under a smooth morphism $$\varphi:X\to Y$$ between compact complex analytic manifolds. It is shown that, in general, the ampleness of $$L$$ does not imply that of the direct image $$\varphi_*L$$ but only that of the direct image of the adjoint line bundle $$\varphi_* (K_{X/Y}\otimes L)$$.

##### MSC:
 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 32C35 Analytic sheaves and cohomology groups 32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)
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