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arXiv · 1805.02277

On the Kodaira problem for uniruled K\"ahler spaces

Patrick Graf·Martin Schwald
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Abstract

We discuss the Kodaira problem for uniruled K\"ahler spaces. Building on a construction due to Voisin, we give an example of a uniruled K\"ahler 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.

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Patrick Graf, Martin Schwald. 2018-05-06. On the Kodaira problem for uniruled K\"ahler spaces. https://doi.org/10.4310/arkiv.2020.v58.n2.a3

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