A simple remark on a flat projective morphism with a Calabi-Yau fiber
classification
🧮 math.AG
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fibercalabi-yauconnectedflatprojectivesurfaceanswerasked
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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.
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