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 some theories for calculating the Picard groups of the Calabi–Yau manifolds obtained in this method. As an application, we construct more than two hundred new families of Calabi–Yau 3-folds with Picard number one that have different Hodge numbers (h’s). We also exhibit a Hilbert scheme that contains more than one hundred different families of Calabi–Yau 3-folds with Picard number one. One of the Calabi-Yau 3-folds has exotic Hodge numbers: h = h = 1.