Holomorphic one-forms without zeros on K\"ahler manifolds of Kodaira codimension one

TL;DR

This paper classifies compact K"ahler manifolds of Kodaira codimension one that possess a holomorphic one-form without zeros, providing a bimeromorphic classification for such structures.

Contribution

It offers the first comprehensive bimeromorphic classification of these manifolds with zero-free holomorphic one-forms.

Findings

Classification of manifolds with zero-free holomorphic one-forms

Identification of geometric structures related to Kodaira codimension one

Insights into the bimeromorphic properties of such K"ahler manifolds

Abstract

We give a bimeromorphic classification of compact K\"ahler manifolds of Kodaira codimension one that admit a holomorphic one form without zeros.