Compact Kähler manifolds with compactifiable universal cover

Abstract

Let X be a compact Kähler 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.

With an appendix by Frédéric Campana (entitled "Abelianity, Iitaka and S conjectures"). 17 pages, no figure