Arkiv för Matematik
Volume 58 (2020)
On the Kodaira problem for uniruled Kähler spaces
Pages: 267 – 284
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.
Kähler manifolds, uniruled Kähler spaces, Mori fibrations, algebraic approximation, small projective deformations, locally trivial deformations
2010 Mathematics Subject Classification
14E30, 32G05, 32J27
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.
Received 14 June 2019
Received revised 24 September 2019
Accepted 13 March 2020
Published 3 November 2020