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)


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.


Normal Form Holomorphic Function Volume Form Poisson Structure Resonance Number 
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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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