Real Algebraic and Analytic Geometry
Submission: 2006, May 26.
We study the multiplicity modulo 2 of real algebraic hypersurfaces. We prove that under some assumptions on the singularity it is preserved through a semi-algebraic bi-Lipschitz homeomorphism of $S^n$. In a first part we find a part of the tangent cone enclosing the multiplicity mod 2 and prove that it is an equivariant subset of $S^n$. Studying equivariant submanifolds of $S^n$ we are able to conclude about its invariance through semi-algebraic bi-Lipschitz homeomorphisms whenever the tangent cone has an isolated singularity at the origin.
Mathematics Subject Classification (2000): 14P05, 14C17, 55P92.
Keywords and Phrases: Real algebraic hypersurfaces, multpilicity, metric invariants, equivariant subsets.
Full text, 11p.: dvi 59k, ps.gz 164k, pdf 200k.