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October 2020 On the Kodaira problem for uniruled Kähler spaces
Patrick Graf, Martin Schwald
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Ark. Mat. 58(2): 267-284 (October 2020). DOI: 10.4310/ARKIV.2020.v58.n2.a3


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.


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Patrick Graf. Martin Schwald. "On the Kodaira problem for uniruled Kähler spaces." Ark. Mat. 58 (2) 267 - 284, October 2020.


Received: 14 June 2019; Revised: 24 September 2019; Published: October 2020
First available in Project Euclid: 16 January 2021

Digital Object Identifier: 10.4310/ARKIV.2020.v58.n2.a3

Primary: 14E30 , 32G05 , 32J27

Keywords: algebraic approximation , Kähler manifolds , locally trivial deformations , Mori fibrations , small projective deformations , uniruled Kähler spaces

Rights: Copyright © 2020 Institut Mittag-Leffler


Vol.58 • No. 2 • October 2020
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