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If a K3 surface is a fiber of a flat projective morphisms over a connectednoetherian scheme over the complex number field, then any smooth connectedfiber is also a K3 surface. Observing this, Professor Nam-Hoon Lee asked if thesame is true for higher dimensional Calabi-Yau fibers. We shall give anexplicit negative answer to his question as well as a proof of his initialobservation.

A simple remark on a flat projective morphism with a Calabi-Yau fiber