Stable mappings of discriminant varieties

Smooth mappings defined on discriminant varieties of -versal unfoldings of isolated singularities arise in many interesting geometrical contexts, for example when classifying outlines of smooth surfaces in 3 and their duals, or wave-front evolution [1, 2, 5]. In three previous papers we have classified various stable mappings on discriminants. When the isolated singularity is weighted homogeneous the discriminant is not a local smooth product, and this makes the classification of stable germs considerably easier than in general. Moreover, discriminants arising from weighted homogeneous singularities predominate in low dimensions, so such classifications are very useful for applications.