English

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

Algebraic Geometry 2015-05-18 v2

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.

Keywords

Cite

@article{arxiv.1002.2810,
  title  = {A simple remark on a flat projective morphism with a Calabi-Yau fiber},
  author = {Keiji Oguiso},
  journal= {arXiv preprint arXiv:1002.2810},
  year   = {2015}
}

Comments

8 pages, main theorem is generalized, one more remark is added, mis-calculation and typos are corrected etc.