Kodaira Additivity, Birational Isotriviality, and Specialness

Abstract

. We show, using [14], that a smooth projective fibration f : X → Y between connected complex quasi-projective manifolds satisfies the equality κ ( X ) = κ ( X y ) + κ ( Y ) of Logarithmic Kodaira dimensions if its fibres X y admit a good minimal model. Without the last assumption, this was conjectured in [11]. Sev-eral cases are established in [13], which inspired the present text. Although the present results overlap with those of [13] in the projective case, the approach here is different, based on the rôle played by birationally isotrivial fibrations, special manifolds and the core map of Y introduced and constructed in [3].