Albanese map of special manifolds: A correction

TL;DR

This paper proves that special compact Kähler manifolds fibrated onto Abelian varieties lack multiple fibers in codimension one, extending prior results and correcting an incomplete proof in earlier literature.

Contribution

It establishes a new property of special Kähler manifolds related to their fibrations, strengthening previous theorems and providing a corrected proof.

Findings

No multiple fibers in codimension one for fibrations of special Kähler manifolds onto Abelian varieties.

Extension of Kawamata and Viehweg's results for manifolds with zero Kodaira dimension.

Correction of an incomplete proof in earlier work.

Abstract

We show that any fibration of a 'special' compact K{\"a}hler manifold X onto an Abelian variety has no multiple fibre in codimension one. This statement strengthens and extends previous results of Kawamata and Viehweg when $\kappa$(X) = 0. This also corrects the proof given in [2], 5.3 which was incomplete.