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On the Kodaira problem for uniruled Kähler spaces

Patrick Graf Department of Mathematics, University of Utah, Salt Lake City, Ut., U.S.A. Martin Schwald Fakultät für Mathematik, Universität Duisburg–Essen, Essen, Germany

Complex Variables and Complex Analysis Algebraic Geometry mathscidoc:2203.08003

Arkiv for Matematik, 58, (2), 267-284, 2020.11
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.
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@inproceedings{patrick2020on,
  title={On the Kodaira problem for uniruled Kähler spaces},
  author={Patrick Graf, and Martin Schwald},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311095347501748943},
  booktitle={Arkiv for Matematik},
  volume={58},
  number={2},
  pages={267-284},
  year={2020},
}
Patrick Graf, and Martin Schwald. On the Kodaira problem for uniruled Kähler spaces. 2020. Vol. 58. In Arkiv for Matematik. pp.267-284. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311095347501748943.
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