On the Local Geometry of a Bihamiltonian Structure

  • Israel M. Gelfand
  • Ilya Zakharevich


We give several examples of bihamiltonian manifolds and show that under very mild assumptions a bihamiltonian structure in “general position” is locally of one of these types. This shows, in particular, that a bihamiltonian manifold in general position is always a moduli space of some kind. In the even-dimensional case it is a Hubert scheme of a surface, in the odd-dimensional case it is a sub- cotangent bundle of a moduli space of rational curves on a surface.


Poisson Bracket Poisson Structure Regular Point Cotangent Bundle Hilbert Scheme 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Israel M. Gelfand
    • 1
  • Ilya Zakharevich
    • 2
  1. 1.Dept. of MathematicsRutgers University, Hill CenterNew BrunswickUSA
  2. 2.Dept. of MathematicsMITCambridgeUSA

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