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Kähler spaces and proper open morphisms. (English) Zbl 0632.53059

We prove among other results: (1) If \(\pi\) : \(X\to X'\) is a proper open surjective morphism of complex spaces with X Kähler and X’ reduced then, if either \(\pi\) is flat or X’ normal, X’ is Kähler. (2) If X is a Kähler space then the Barlet space \(B_ m(X)\) of compact complex m- cycles of X is Kähler. (3) Any reduced compact complex space in Fujiki’s class \({\mathcal C}\) (holomorphic image of a compact Kähler space) is bimeromorphically equivalent to a compact Kähler manifold.

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
32C15 Complex spaces
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