# The fundamental group of compact Kähler threefolds

Abstract : Let $X$ be a compact Kähler manifold of dimension three. We prove that there exists a projective manifold $Y$ such that $\pi_1(X)\simeq \pi_1(Y)$. 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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Document type :
Journal articles
Domain :

https://hal.univ-cotedazur.fr/hal-01415323
Contributor : Andreas Höring <>
Submitted on : Wednesday, December 16, 2020 - 11:39:23 AM
Last modification on : Tuesday, February 16, 2021 - 3:30:02 PM

### Citation

Benoît Claudon, Andreas Höring, Hsueh-Yung Lin. The fundamental group of compact Kähler threefolds. Geometry and Topology, Mathematical Sciences Publishers, 2019, 23 (7), pp.3233-3271. ⟨10.2140/gt.2019.23.3233⟩. ⟨hal-01415323v4⟩

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