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Versal deformations of powers of volume forms

  • V. P. Kostov
  • S. K. Lando
Conference paper
Part of the Progress in Mathematics book series (PM, volume 109)

Abstract

Deformations of powers of volume forms of the kind
$$ F\left( {x,\lambda } \right){{\left( {dx} \right)}^{\alpha }},x \in {{C}^{n}},F\left( {x,0} \right) = f\left( x \right),dx = d{{x}_{1}} \wedge ... \wedge d{{x}_{n}},\alpha \in C $$
are investigated. If f has an isolated singularity of multiplicity μ at the origin, then the form f(x)(dx) α has a μ-parameter versal deformation for almost every value of α. Exceptional values of α form a discrete set of negative rational numbers. Given f, the versal deformation can be obtained algorithmically. For non-exceptional values of α it is the same as the versal deformation of the germ of a function f.

Keywords

Normal Form Holomorphic Function Volume Form Poisson Structure Resonance Number 
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.

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Copyright information

© Birkhäuser Boston 1993

Authors and Affiliations

  • V. P. Kostov
    • 1
  • S. K. Lando
    • 2
  1. 1.Laboratoire de Mathématiques, U.R.A. du C.N.R.S. No 168Université de Nice — Sophia AntipolisNice Cedex 02France
  2. 2.Institute of New TechnologiesMoscowUSSR

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