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Fernandes, A.; Edson Sampaio, J.

Multiplicity of analytic hypersurface singularities under bi-Lipschitz homeomorphisms. (English) Zbl 1353.14005

J. Topol. 9, No. 3, 927-933 (2016).
The authors consider a metric analogue of Zariski’s multiplicity question: have two reduced hypersurface singularities, which are bi-Lipschitz \(\mathcal V\)-equivalent, the same multiplicity? They first show that the answer is yes if and only if the result holds for irreducible homogeneous polynomials. As corollary they obtain a positive answer for the case that all components of the tangent cone have isolated singularities, and for surface singularities without any restriction.
Reviewer: Jan Stevens (Göteborg)

Cited in 13 Documents

MSC:

14B05 Singularities in algebraic geometry
32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants

Keywords:

Zariski’s multiplicity conjecture; bi-Lipschitz equivalence; Lelong numbers
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References:

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