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Towards a Mori theory on compact Kaehler threefolds, III

Thomas Peternell
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Abstract

We prove abundance for a minimal Kaehler threefold which is not both simple and non-Kummer. Recall that a variety is simple if there is no compact subvariety of positive dimension through a sufficiently general point . Furthermore we prove that a smooth compact Kaehler threefold whose canonical bundle is not nef, carries a contraction unless (possibly) the manifold is simple non-Kummer. It is generally conjectured that simple threefolds must be Kummer.

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Thomas Peternell. 1999-02-26. Towards a Mori theory on compact Kaehler threefolds, III. https://arxiv.org/abs/math/9902149

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