Many singularities are not stably equivalent to Newton-non-degenerate singularities

Abstract

This paper has been withdrawn. Consider an isolated complex hypersurface singularity, f(x_1,..,x_n)=0. For Newton-non-degenerate singularities the local topology is completely determined by an associated polyhedral object, the Newton diagram. "Most" singularities are not Newton-non-degenerate, for any choice of local coordinates. An old question of Arnol'd asks whether for any hypersurface singularity there exists a stabilization, f(x_1,...,x_n)+z^2_1+...+z^2_r, that becomes Newton-non-degenerate after some change of coordinates. The answer is: "totally no". We give some simple obstructions and present particular examples of plane curve singularities that have no Newton-non-degenerate stabilization (in any local coordinates).