On the Local Geometry of a Bihamiltonian Structure
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.
KeywordsPoisson Bracket Poisson Structure Regular Point Cotangent Bundle Hilbert Scheme
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