Volume 23, issue 7 (2019)

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The fundamental group of compact Kähler threefolds

Benoît Claudon, Andreas Höring and Hsueh-Yung Lin

Geometry & Topology 23 (2019) 3233–3271

Let X be a compact Kähler manifold of dimension three. We prove that there exists a projective manifold Y such that π1(X) π1(Y ). We also prove the bimeromorphic existence of algebraic approximations for compact Kähler manifolds of algebraic dimension dimX 1. Together with the work of Graf and the third author, this settles in particular the bimeromorphic Kodaira problem for compact Kähler threefolds.

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fundamental group, compact Kähler manifolds, algebraic approximations, elliptic fibrations
Mathematical Subject Classification 2010
Primary: 14D07, 32J17, 32J27, 32Q55
Received: 25 July 2017
Revised: 20 August 2018
Accepted: 29 April 2019
Published: 30 December 2019
Proposed: Dan Abramovich
Seconded: Anna Wienhard, John Lott
Benoît Claudon
Université Rennes 1
Institut Universitaire de France
Andreas Höring
Université Côte d’Azur
Laboratoire Jean-Alexandre Dieudonné
Institut Universitaire de France
Hsueh-Yung Lin
Mathematisches Institut der Universität Bonn