ABSTRACT
The main result amounts determine the Zariski's tangent space at a point of a Flag Schubert variety by a combinatorial procedure thus allowing the characterization of the Singular cells contained in a Schubert variety. This determination depends on the combinatorial structure of the smooth resolutions, more precisely on the combinatorial fibers. It is known that the smooth resolution associated with a Schubert variety in the former chapter contains an open subvariety isomorphic to the corresponding Schubert cell and that this cell is isomorphic to its pull-back. Hence, this pull-back is equal to this open subvariety. The critical Schubert cells contained in the smooth open set of a Schubert variety are determined by the Zariski's tangent space at a point, combinatorially calculated, and this without any characteristic restrictions on the base field k.
