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The dual Kaehler cone of compact Kaehler threefolds

Keiji Oguiso·Thomas Peternell
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Abstract

We consider a compact Kaehler manifold whose dual Kaehler cone contains a rational interior point. The general problem we have in mind is how far the manifold is from being projective; i.e. we ask for the algebraic dimension. We prove e.g. that if the interior point is represented by an effective curve in dimension 3, then the manifold has algebraic dimension at least 2 unless the variety is a so-called simple non-Kummer 3-fold. We also investigate 3-folds containing curves with ample normal bundle. It seems likely that examples with algebraic dimension 2 really exist.

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Keiji Oguiso, Thomas Peternell. 2004-06-11. The dual Kaehler cone of compact Kaehler threefolds. https://arxiv.org/abs/math/0107224

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