We discuss the Kodaira problem for uniruled Kähler spaces. Building on a construction due to Voisin, we give an example of a uniruled Kähler space $X$ such that every run of the $K_X$-MMP immediately terminates with a Mori fibre space, yet $X$ does not admit an algebraic approximation. Our example also shows that for a Mori fibration, approximability of the base does not imply approximability of the total space.

中文翻译：

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关于未经激励的Kähler空间的Kodaira问题

我们讨论了无扰动的Kähler空间的Kodaira问题。我们以Voisin的构造为基础，给出了一个不受激励的Kähler空间$ X $的示例，这样，$ K_X $ -MMP的每次运行都立即以Mori纤维空间终止，但是$ X $不允许代数近似。我们的示例还显示，对于Mori纤维，基部的近似性并不意味着总空间的近似性。