Real double-points of deformations of -simple map-germs from n to 2n

Abstract

AbstractThe only stable singularities of a real map-germ $f:{\mathbb R} ^n\to{\mathbb R} ^{2n}$ are isolated transverse double-points. All ${{\cal A}}$-simple germs f have a deformation with the maximal number d(f) of real double-points (this is a partial generalization to higher n of the result of A'Campo [1] and Gusein-Zade [13] that all plane curve-germs have a deformation with δ real double points, with the extra hypothesis of ${{\cal A}}$-simplicity). The proof of this result is based on a classification of all ${{\cal A}}$-simple orbits.