Abstract
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.
Funding Statement
The first author was partially supported by a DFG Research Fellowship. The second author was partially supported by the DFG Collaborative Research Centre SFB/TR 45.
Citation
Patrick Graf. Martin Schwald. "On the Kodaira problem for uniruled Kähler spaces." Ark. Mat. 58 (2) 267 - 284, October 2020. https://doi.org/10.4310/ARKIV.2020.v58.n2.a3
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