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arXiv · 1012.0109

New Constructions of Complex Manifolds

Jinxing Xu
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Abstract

For a generic anti-canonical hypersurface in each smooth toric Fano 4-fold with rank 2 Picard group, we prove there exist three isolated rational curves in it. Moreover, for all these 4-folds except one, the contractions of generic anti-canonical hypersurfaces along the three rational curves can be deformed to smooth threefolds diffeomorphic to connected sums of S^{3} \times S^{3}. In this manner, we obtain complex structures with trivial canonical bundles on some connected sums of S^{3} \times S^{3}. This construction is an analogue of that in Friedman [7], Lu and Tian [12] which used only quintics in P^{4}.

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Jinxing Xu. 2010-12-01. New Constructions of Complex Manifolds. https://arxiv.org/abs/1012.0109

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