Real Algebraic and Analytic Geometry |

Multiplicity mod 2 as a metric invariant.

e-mail:

homepage: http://www.im.uj.edu.pl/GuillaumeValette

Submission: 2006, May 26.

*Abstract:
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.

Server Home Page