Multiplicity of complex analytic sets and bilipshitz maps. (English) Zbl 0982.32026

Comte, Georges

Fukuda, T. (ed.) et al., Real analytic and algebraic singularities. Harlow: Longman. Pitman Res. Notes Math. Ser. 381, 182-188 (1998).

The Zariski multiplicity conjecture states that the multiplicity of a hypersurface singularity is a topological invariant. In this paper, the author shows that the multiplicity is invariant under bilipschitz maps, where the Lipschitz constants satisfy a certain inequality. The constancy of the multiplicity along stratum of a Lipschitz trivial stratification is proved.
For the entire collection see [Zbl 0882.00014].

Reviewer: T.de Jong (Saarbrücken)

MSC:

32S25

Complex surface and hypersurface singularities

Keywords:

Zariski multiplicity conjecture; bilipschitz maps