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Journal of Geometric Analysis

, Volume 21, Issue 3, pp 767–782 | Cite as

Isolated Hypersurface Singularities and Special Polynomial Realizations of Affine Quadrics

  • G. Fels
  • A. Isaev
  • W. Kaup
  • N. Kruzhilin
Article

Abstract

Let V, \(\tilde{V}\) be hypersurface germs in ℂ m , each having a quasi-homogeneous isolated singularity at the origin. We show that the biholomorphic equivalence problem for V, \(\tilde{V}\) reduces to the linear equivalence problem for certain polynomials P, \(\tilde{P}\) arising from the moduli algebras of V, \(\tilde{V}\). The polynomials P, \(\tilde{P}\) are completely determined by their quadratic and cubic terms, hence the biholomorphic equivalence problem for V, \(\tilde{V}\) in fact reduces to the linear equivalence problem for pairs of quadratic and cubic forms.

Keywords

Isolated hypersurface singularities Gorenstein algebras 

Mathematics Subject Classification (2000)

32S25 13H10 

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Copyright information

© Mathematica Josephina, Inc. 2011

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität TübingenTübingenGermany
  2. 2.Department of MathematicsThe Australian National UniversityCanberraAustralia
  3. 3.Department of Complex AnalysisSteklov Mathematical InstituteMoscowRussia

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