Right simple singularities in positive characteristic

We classify isolated hypersurface singularites over an algebraically closed field of characteristic $p>0$ w.r.t. right equivalence. The corresponding classification over the real and complex numbers was achieved by V. I. Arnold in his pioneering work in the mid sixties. A surprising fact is that for every fixed $p>0$ there are only finitely many classes of the so called simple singularities. In particular, only finitely many of the ADE singularities have finite deformation type. This stands in strict contrast to Arnold's result in characteristic 0 where the simple singularities are exactly the ADE singularities.