Multiplicity of singularities is not a bi-Lipschitz invariant
Mathematische Annalen, 2020•Springer
… It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove
this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic
singularities with different values of multiplicity. … The present paper shows that the
multiplicity of complex algebraic sets is not a bi-Lipschitz invariant for the sets of dimension
bigger or equal to three. Moreover, we show that there exists an infinite family of 3-dimensional
germs, such that all of them are …
this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic
singularities with different values of multiplicity. … The present paper shows that the
multiplicity of complex algebraic sets is not a bi-Lipschitz invariant for the sets of dimension
bigger or equal to three. Moreover, we show that there exists an infinite family of 3-dimensional
germs, such that all of them are …
Abstract
It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.
Springer
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