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

Relative adjoint transcendental classes and Albanese maps of compact Kaehler manifolds with nef Ricci curvature