The dual Kaehler cone of compact Kaehler threefolds

Details The dual Kaehler cone of compact Kaehler threefolds The dual Kaehler cone of compact Kaehler threefolds

2001-07-31

arxiv.org/abs/math/0107224v3

Mathematics

Algebraic Geometry

laTeX, 21 pages, final version, to appear in Communications in Analysis and Geometry

Scientific paper

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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