Quelques propri\'et\'es de stabilit\'e des vari\'et\'es sp\'eciales

TL;DR

This paper proves that the general fibers of the Albanese morphism of a projective special manifold are also special, using a boundary version of Iitaka's conjecture, with implications for algebraic geometry.

Contribution

It establishes the stability of the 'special' property under the Albanese morphism for projective manifolds, extending previous understanding in the field.

Findings

Fibers of the Albanese morphism are also special.

Uses boundary version of Iitaka's conjecture.

Discusses consequences for algebraic geometry.

Abstract

We show that the general fibres of the Albanese morphism of a projective special manifold are special as well (a question raised by the first-named author). The main ingredient of the proof is a version (established by Birkar and Chen) with boundary of the famous conjecture of Iitaka on the subadditivity of the Kodaira dimension in an algebraic fibre space. Some consequences of our main result are discussed.