Projectivity criteria for K\"ahler morphisms

TL;DR

This paper establishes new projectivity criteria for fibrations between mildly singular compact K"ahler spaces, extending classical results and showing that the MRC fibration always admits a projective model.

Contribution

It provides the first relative versions of Kodaira and Moishezon's projectivity criteria for K"ahler fibrations, with applications to MRC fibrations.

Findings

Established two projectivity criteria for K"ahler fibrations.

Proved the MRC fibration has a projective model.

Abstract

In this short note we prove two projectivity criteria for fibrations between mildly singular compact K\"ahler spaces. They are the relative versions of the celebrated criteria of Kodaira and Moishezon. As an application we obtain that the MRC fibration always has a model that is a projective morphism.