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This paper has been withdrawn.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).
Keywords
Cite
@article{arxiv.1401.6781,
title = {Many singularities are not stably equivalent to Newton-non-degenerate singularities},
author = {Anna Gourevitch and Dmitry Kerner},
journal= {arXiv preprint arXiv:1401.6781},
year = {2014}
}
Comments
This paper has been withdrawn by the authors. Many thanks to J.Stevens for pointing the error in the proof