ABSTRACT
This chapter provides the configurations variety giving a smooth resolution of singularities for a Schubert variety is, in fact, isomorphic to a gallery variety given by a minimal generalized gallery of types. The gallery of types g(M) depends solely on M. A generalized gallery of chains of adapted subspaces is first obtained from this configuration, giving rise, after reduction, to that minimal generalized gallery. It is given another example of a configurations variety and a corresponding isomorphic gallery variety. These two examples show, for the linear group, the role played by the geometry of the Tits building in unifying the constructions of configuration varieties. The chapter describes how the minimal generalized gallery associated with a Relative position matrix. It talks about the Nash smooth resolutions, and examines how the Nash minimal gallery associated with a Relative position matrix.
