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Published online by Cambridge University Press: 01 November 1997
Let X be a smooth projective manifold over the complex number field [Copf] and L a Cartier divisor on X. Then (X, L) is called a polarized (resp. quasi-polarized) manifold if L is ample (resp. nef and big). For a polarized manifold (X, L), Takao Fujita introduced the notion of the Kodaira energy κε(X, L). The Kodaira energy of (X, L) is thought to have some interesting phenomena if κ(X)=−∞ (for example, Spectrum Conjecture which was proposed by T. Fujita). In order to study the Kodaira energy of (X, L), we consider the case in which X has a fibre space, that is, there exist a smooth projective manifold Y with dimX>dimY[ges ]1 and a surjective morphism f[ratio ]X→Y with connected fibres. In this case we introduce the notion of relative Kodaira energy and study some property of it. By using some results of relative Kodaira energy, we study some properties of the Kodaira energy.