We give a characterization of the irreducible components of a Weierstrass-type (W-type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a component of a W-type variety, this description may be applied to any such variety.
In this Note, we announce several results concerning basic properties of the spaces of morphisms between real algebraic varieties. Our results show a surprising intrinsic rigidity of Real Algebraic Geometry and illustrate the great distance which, in some sense, exists between this geometry and Real Nash one. Let us give an example of this rigidity. An affine real algebraic variety is rigid if, for each affine irreducible real algebraic variety , the set of all nonconstant regular morphisms from...