2022/07/12 by Frederic Bruno Campana, Campana, Frederic Bruno
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds
paper · doi:10.48550/arxiv.2207.05412
openalex publication_date 2022/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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]. Several 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].