IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-31925-9_9.html
   My bibliography  Save this book chapter

Bi-Lipschitz Invariance of the Multiplicity

In: Handbook of Geometry and Topology of Singularities IV

Author

Listed:
  • Alexandre Fernandes

    (Universidade Federal do Ceará, Departamento de Matemática)

  • José Edson Sampaio

    (Universidade Federal do Ceará, Departamento de Matemática)

Abstract

The multiplicity of an algebraic curve C in the complex plane at a point p on that curve is defined as the number of points that occur at the intersection of C with a general complex line that passes close to the point p. It is shown that p is a singular point of the curve C if and only if this multiplicity is greater than or equal to 2, in this sense, such an integer number can be considered as a measure of how singular can be a point of the curve C. In these notes, we address the classical concept of multiplicity of singular points of complex algebraic sets (not necessarily complex curves) and we approach the nature of the multiplicity of singular points as a geometric invariant from the perspective of the Multiplicity Conjecture (Zariski 1971). More precisely, we bring a discussion on the recent results obtained jointly with Lev Birbrair, Javier Fernández de Bobadilla, Lê Dũng Tráng and Mikhail Verbitsky on the bi-Lipschitz invariance of the multiplicity.

Suggested Citation

  • Alexandre Fernandes & José Edson Sampaio, 2023. "Bi-Lipschitz Invariance of the Multiplicity," Springer Books, in: José Luis Cisneros-Molina & Lê Dũng Tráng & José Seade (ed.), Handbook of Geometry and Topology of Singularities IV, chapter 0, pages 463-496, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-31925-9_9
    DOI: 10.1007/978-3-031-31925-9_9
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-031-31925-9_9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.