An approach to the abundance conjecture for Kähler varieties via algebraic reduction

In this article, we establish a strategy to the abundance conjecture for Kähler varieties via induction on algebraic dimension. Our strategy is to reduce the abundance conjecture for Kähler varieties to the abundance conjecture for projective varieties using the algebraic reduction fibration. In dimension 4, we apply our inductive strategy to obtain some cases of the abundance conjecture for Kähler fourfolds that are not algebraic or have trivial $K_X$.