Shade singularities (Q1364377)

We classify stable singularities that appear in pictures of illuminated surfaces; to a comprehensive mathematical model which involves also the shadow that the surface casts on itself, we associate a classification problem in the space of germs of real analytic functions: we define an appropriate relation equivalence (a refinement of \({\mathcal A}\)-equivalence) and we give the list of its open classes. These classes give the genetic local aspects of illuminated surfaces.