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Multiplicity of singularities is not a bi-Lipschitz invariant

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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.

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Authors and Affiliations

  1. Instituto Nacional de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina, 110 Jardim Botânico, CEP 22460-320, Rio de Janeiro, RJ, Brasil

    Misha Verbitsky

  2. Laboratory of Algebraic Geometry, Department of Mathematics, National Research University Higher School of Economics, 6 Usacheva street, Moscow, Russia

    Misha Verbitsky

  3. Departamento de Matemática, Universidade Federal do Ceará, Rua Campus do Pici, s/n, Bloco 914 Pici, CEP 60440-900, Fortaleza, CE, Brazil

    Lev Birbrair, Alexandre Fernandes & J. Edson Sampaio

  4. Basque Center for Applied Mathematics (BCAM), Mazarredo, 14, E48009, Bilbao, Basque, Spain

    J. Edson Sampaio

Authors
  1. Lev Birbrair
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  2. Alexandre Fernandes
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  3. J. Edson Sampaio
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  4. Misha Verbitsky
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Corresponding author

Correspondence to Lev Birbrair.

Additional information

Communicated by Jean-Yves Welschinger.

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Lev Birbrair: Partially supported by CNPq grant 302655/2014-0. Alexandre Fernandes: Partially supported by CNPq grant grant304221/2017-9 and by CAPES-BRASIL Finance Code 001. J. Edson Sampaio: Partially supported by CNPq-Brazil grant 303811/2018-8, by the ERCEA 615655 NMST Consolidator Grant and also by the Basque Government through the BERC 2018-2021 program and Gobierno Vasco Grant IT1094-16, by the Spanish Ministry of Science, Innovation and Universities: BCAM Severo Ochoa accreditation SEV-2017-0718. Misha Verbitsky: Partially supported by the Russian Academic Excellence Project ‘5-100’, FAPERJ E-26/202.912/2018 and CNPq - Process 313608/2017-2.

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Birbrair, L., Fernandes, A., Sampaio, J.E. et al. Multiplicity of singularities is not a bi-Lipschitz invariant. Math. Ann. 377, 115–121 (2020). https://doi.org/10.1007/s00208-020-01958-x

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  • DOI: https://doi.org/10.1007/s00208-020-01958-x

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