Calabi–yau Construction by Smoothing Normal Crossing Varieties

We investigate a method of construction of Calabi–Yau manifolds, that is, by smoothing normal crossing varieties. We develop theories for calculating the Picard groups of the Calabi–Yau manifolds obtained in this method. As an application, we show that many examples of Kawamata and Namikawa are different Calabi–Yau three-folds although they have same Hodge numbers.