ABSTRACT
A smooth resolution of singularities for a Schubert variety in a flag variety is constructed in terms of a Configurations variety directly obtained from its Relative Position Matrix. This is a canonical smooth resolution whose construction is suggested by our indexation of Schubert varieties in Flag varieties by Relative Position Matrices. R. Thom attempts to give a description of the singularities of a differentiable function by means of an iterative procedure involving functions into Grassmannians. These functions appear as locally classifying mappings associated with the family of tangent spaces to the graph of this function. Its generic singularities are thus described by a "Stratification" defined by the Pull-Backs of Special Schubert varieties by these classifying mappings. The chapter summarizes the description of the constructions in scheme theory. The decomposition of in terms of a sequence of fibrations, namely and, may be easily transposed into the scheme theoretic frame.
