A simple remark on a flat projective morphism with a Calabi-Yau fiber
arXiv:1002.2810 · doi:10.1007/s11425-010-4115-3
Abstract
If a K3 surface is a fiber of a flat projective morphisms over a connected noetherian scheme over the complex number field, then any smooth connected fiber is also a K3 surface. Observing this, Professor Nam-Hoon Lee asked if the same is true for higher dimensional Calabi-Yau fibers. We shall give an explicit negative answer to his question as well as a proof of his initial observation.
8 pages, main theorem is generalized, one more remark is added, mis-calculation and typos are corrected etc.