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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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