The fundamental group of compact Kähler threefolds

Claudon, Benoît; Höring, Andreas; Lin, Hsueh-Yung

doi:10.2140/gt.2019.23.3233

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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

DOI: 10.2140/gt.2019.23.3233

Abstract

Let $X$ be a compact Kähler manifold of dimension three. We prove that there exists a projective manifold $Y$ such that $π_{1} (X) ≃ π_{1} (Y)$ . We also prove the bimeromorphic existence of algebraic approximations for compact Kähler manifolds of algebraic dimension $dim X - 1$ . 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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Keywords

fundamental group, compact Kähler manifolds, algebraic approximations, elliptic fibrations

Mathematical Subject Classification 2010

Primary: 14D07, 32J17, 32J27, 32Q55

References

Publication

Received: 25 July 2017

Revised: 20 August 2018

Accepted: 29 April 2019

Published: 30 December 2019

Proposed: Dan Abramovich

Seconded: Anna Wienhard, John Lott

Authors

Benoît Claudon
Université Rennes 1 IRMAR-UMR 6625 Rennes France	Institut Universitaire de France

Andreas Höring
Université Côte d’Azur CNRS Laboratoire Jean-Alexandre Dieudonné Nice France	Institut Universitaire de France

Hsueh-Yung Lin
Mathematisches Institut der Universität Bonn Bonn Germany

Volume 23, issue 7 (2019)