Abstract
Given a surjective holomorphic map between two compact Kaehler manifolds, we investigate the positivity properties of relative adjoint transcendental classes which are inherited from similar fiberwise properties. As a consequence, we solve a problem proposed by J.-P. Demailly, T. Peternell and M. Schneider concerning the Albanese morphism of Kaehler manifolds with nef anticanonical class.
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