In this article the authors show the proofs of conjectures formulated by Fujita ([6]) and propose to adopt numerical equivalence classes of divisors in place of linear equivalence classes when classifying algebraic varieties, since Enault-Viehweg type vanishing theorems ([11] hold up to numerical equivalence. Zariski decomposition are treated in numerical equivalence. 0ne of the main concerns in birational geometry is whether the amplitude of the variation of fibres should be bounded above by the difference between the relative Kodaira dimensions of the whole and the generic fibre ([10], [11]). This theme can be transferred to new relative Kodaira dimensions defined by numerical equivalence classes ([9])
