Compact K\"ahler manifolds with compactifiable universal cover

TL;DR

This paper explores the properties of compact Kähler manifolds with universal covers that can be compactified, proposing a conjecture about their fundamental groups and linking it to Iitaka's conjecture.

Contribution

It introduces a new conjecture relating the fundamental group of such manifolds to being almost abelian, reducing the problem to a classical conjecture of Iitaka.

Findings

Proposes that the fundamental group is almost abelian under the given conditions

Reduces the problem to a classical conjecture of Iitaka

Provides a new perspective on the structure of Kähler manifolds with compactifiable universal cover

Abstract

Let X be a compact K\"ahler manifold such that the universal cover admits a compactification. We conjecture that the fundamental group is almost abelian and reduce it to a classical conjecture of Iitaka.