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arXiv · 1612.04224

The fundamental group of compact K{ä}hler threefolds

Benoît Claudon·Andreas Höring·Hsueh-Yung Lin
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Abstract

Let $X$ be a compact K{ä}hler manifold of dimension three. We prove that there exists a projective manifold $Y$ such that $π\_1(X)\simeq π\_1(Y)$. We also prove the bimeromorphic existence of algebraic approximations for compact K{ä}hler 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 K{ä}hler threefolds.

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Benoît Claudon, Andreas Höring, Hsueh-Yung Lin. 2018-03-02. The fundamental group of compact K{ä}hler threefolds. https://doi.org/10.2140/gt.2019.23.3233

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