On fibrations whose geometric fibers are nonreduced

2009/02/25 by Schroeer, Stefan · 1 citation
#14A15 #14D05 #14J70 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0902.4393

Abstract

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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• Varieties with nef anticanonical divisors and Albanese morphisms of relative dimension one in positive characteristic

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