ag.algebraic geometry – Examples of compact Kähler manifolds with semi-ample canonical bundle

Let $$(X, omega)$$ be a compact Kähler manifold. The canonical bundle $$K_X$$ is said to be semi-ample if a sufficiently high power of it furnishes a holomorphic map $$f : X to Y$$ onto a normal projective variety $$Y$$, with the dimension of $$Y$$ being the Kodaira dimension of $$X$$. To those in the establishment, $$Y$$ is the canonical model of $$X$$. By adjunction, one can show that $$f : X to Y$$ is a Calabi-Yau fiber space, i.e., $$f$$ is a proper surjective holomorphic map whose smooth fibers have vanishing first Chern class. In particular, compact Kähler manifolds can be constructed by considering such Calabi-Yau fiber spaces.

I would like to collect as many explicit examples of such objects, preferably with $$dim(Y) > 1$$ and $$f$$ not being an elliptic fibration.