Singularities appearing on generic fibers of morphisms between smooth schemes

2006/08/01 by Stefan Schroeer, Schroeer, Stefan · 1 citation
Mathematics · #14B07 #14D06 #14F20 #14G27 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14B07 #msc:14D06 #msc:14F20 #msc:14G27

paper · pdf · doi:10.48550/arxiv.math/0608015

20 pages

arxiv created 2006/08/01 · arxiv updated 2009/12/01

Abstract

I 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.

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