2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221488We 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.17 pagesAlgebraic Geometry14A15, 14D05, 14J70text