%0 Journal Article
%T Stably Newton non-degenerate singularities
%A Jan Stevens
%J Mathematics
%D 2014
%I arXiv
%X We discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. The answer is negative. The easiest example can be given in characteristic $p$: the function $x^p$ is not stably equivalent to a non-degenerate function. To deal with characteristic zero we describe a method to make functions non-degenerate after suspension and give an example of a surface singularity where this method does not work. We conjecture that it is in fact not stably equivalent to a non-degenerate function. We argue that irreducible plane curves with an arbitrary number of Puiseux pairs are stably non-degenerate. As the suspension involves many variables, it becomes very difficult to determine the Newton diagram in general, but the form of the equation indicates that it is non-degenerate.
%U http://arxiv.org/abs/1406.0328v2