Advertisement

The local multiplicity of a holomorphic map

  • V. I. Arnold
  • S. M. Gusein-Zade
  • A. N. Varchenko
Chapter
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

It is proved in this Chapter that the algebraic multiplicity of a holomorphic map coincides with its geometric multiplicity, that is with the index of the singular point of the corresponding holomorphic field. Although this result was known classically it seems that a detailed proof was published only in the paper [139] of V. P. Palamodov. The idea of the elementary proof presented below is due to A. G. Kushnirenko [106].

Keywords

Bilinear Form Finite Type Local Algebra Trace Theorem Source Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • V. I. Arnold
  • S. M. Gusein-Zade
    • 1
  • A. N. Varchenko
    • 2
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Department of MathematicsThe University of North Carolina at Chapel HillChapel HillUSA

Personalised recommendations