Algebraic varieties with quasi-projective universal cover

TL;DR

This paper characterizes when the universal cover of a normal, projective variety is quasi-projective, linking it to the existence of a finite étale cover that forms a fiber bundle over an Abelian variety with simply connected fibers.

Contribution

It provides a precise criterion connecting the quasi-projectivity of the universal cover to the structure of finite étale covers as fiber bundles over Abelian varieties.

Findings

Universal cover is quasi-projective iff a finite étale cover is a fiber bundle over an Abelian variety.

Characterization of universal covers in terms of fiber bundle structures.

Connection between quasi-projectivity and the fiber bundle structure over Abelian varieties.

Abstract

We prove that the universal cover of a normal, projective variety X is quasi-projective if and only if a finite, \'etale cover of X is a fiber bundle over an Abelian variety with simply connected fiber.