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Mathematics > Algebraic Geometry

arXiv:1805.02277 (math)
[Submitted on 6 May 2018 (v1), last revised 6 May 2020 (this version, v2)]

Title:On the Kodaira problem for uniruled Kähler spaces

Authors:Patrick Graf, Martin Schwald
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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.
Comments: Final version, to appear in Arkiv för Matematik
Subjects: Algebraic Geometry (math.AG); Complex Variables (math.CV)
Cite as: arXiv:1805.02277 [math.AG]
  (or arXiv:1805.02277v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.02277
Journal reference: Arkiv for Matematik 58 (2020) no. 2, pp. 267-284
Related DOI: https://doi.org/10.4310/ARKIV.2020.v58.n2.a3

Submission history

From: Patrick Graf [view email]
[v1] Sun, 6 May 2018 20:52:59 UTC (19 KB)
[v2] Wed, 6 May 2020 15:39:29 UTC (19 KB)
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