On fibrations whose geometric fibers are nonreduced

Details On fibrations whose geometric fibers are nonreduced On fibrations whose geometric fibers are nonreduced

2009-02-25

arxiv.org/abs/0902.4393v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

We give a bound on embedding dimensions of geometric generic fibers in terms
of the dimension of the base, for fibrations in positive characteristic. This
generalizes the well-known fact that for fibrations over curves, the geometric
generic fiber is reduced. We illustrate our results with Fermat hypersurfaces
and genus one curves.

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