The fundamental group of compact K{ä}hler threefolds

Abstract

Let $X$ be a compact K{ä}hler 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 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.

27 pages. Main result improved: the algebraic approximation holds now for elliptic compact K{ä}hler manifolds over a projective base in any dimension

References in corpus (1)

• Algebraic approximation of Kähler threefolds of Kodaira dimension zero

Cited by in corpus (4)

• Algebraic approximations of compact Kähler manifolds of algebraic codimension 1
• The Kodaira problem for Kähler spaces with vanishing first Chern class
• Sasaki versus Kähler groups
• Geometric structures in Topology, Geometry, Global Analysis and Dynamics