2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115235I give various criteria for singularities to appear on geometric generic fibers of morphism between smooth schemes in positive characteristics. This involves local fundamental groups, jacobian ideals, projective dimension, tangent and cotangent sheaves, and the effect of Frobenius. As an application, I determine which rational double points do appear on geometric generic fibers.20 pagesAlgebraic Geometry14B07, 14D06, 14F20, 14G27text