Good minimal models with nowhere vanishing holomorphic $1$-forms

TL;DR

This paper characterizes when good minimal models of smooth projective varieties admit nowhere vanishing holomorphic 1-forms, linking such forms to the existence of an analytic fiber bundle structure over an abelian variety.

Contribution

It establishes a precise criterion connecting the existence of nowhere vanishing holomorphic 1-forms on good minimal models to their fiber bundle structure over abelian varieties.

Findings

A good minimal model admits a nowhere vanishing holomorphic 1-form if and only if it is an analytic fiber bundle over an abelian variety.

Holomorphic 1-forms on varieties of general type necessarily have zeros, as shown by Popa and Schnell.

The paper provides a geometric characterization of minimal models with special holomorphic 1-forms.

Abstract

Popa and Schnell show that any holomorphic 1-form on a smooth projective variety of general type has zeros. In this article, we show that a smooth good minimal model has a holomorphic 1-form without zero if and only if it admits an analytic fiber bundle structure over a positive dimensional abelian variety.