Calabi-Yau construction by smoothing normal crossing varieties

Abstract

We investigate a method of construction of Calabi--Yau manifolds, that is, by smoothing normal crossing varieties. We develop some theories for calculating the Picard groups of the Calabi--Yau manifolds obtained in this method. Some applications are included, such as construction of new examples of Calabi--Yau 3-folds with Picard number one with some interesting properties.

A large revision was made. Basically the paper returned to its previous version (v.2). The Kaehlerness arguement in Propositon 9.1 of v.3 needs correction

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• Calabi-Yau manifolds from pairs of non-compact Calabi-Yau manifolds
• Connecting certain rigid birational non-homeomorphic Calabi--Yau threefolds via Hilbert scheme