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Compact K\"ahler 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.Comment: With an appendix by Fr\'ed\'eric Campana (entitled "Abelianity, Iitaka and S conjectures"). 17 pages, no figur

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