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The weak 1-positivity of direct image sheaves. (English) Zbl 0568.14011

The purpose of this paper is to extend some basic result concerning the weak positivity of the direct image sheaves by Viehweg to the case of non-complete varieties. The author shows the additivity of the log- Kodaira dimensions for an algebraic fibre space where the base space is of general type, which Iitaka conjectured. The algebraic technique is fairly similar to the one of Viehweg, the important lemma is due to Kawamata and the soul of the work owes Iitaka’s theory.

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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