Construction of Integral Cohomology in Some Degenerations and Its Application to Smoothing of Degenerate Calabi-yau

A smoothing theorem for normal crossings to Calabi-Yau manifolds was proved by Y. Kawamata and Y. Namikawa ([KaNa]). This paper is a study of the observation that the Picard groups and Chern classes of these Calabi-Yau manifolds are constructible from the normal crossings in such smoothings. We provide and prove the formula for the construction in its full generality and various applications are discussed, including the construction of many new examples of Calabi-Yau 3-folds with Picard number one. With this construction as a starting point, we hope to convince readers that smoothing normal crossings is a promising method of constructing Calabi-Yau manifolds.