On the Local Geometry of a Bihamiltonian Structure

Israel M. Gelfand () and Ilya Zakharevich ()
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Israel M. Gelfand: Rutgers University, Hill Center, Dept. of Mathematics
Ilya Zakharevich: MIT, Dept. of Mathematics

A chapter in The Gelfand Mathematical Seminars, 1990–1992, 1993, pp 51-112 from Springer

Abstract: Abstract 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.

Keywords: Poisson Bracket; Poisson Structure; Regular Point; Cotangent Bundle; Hilbert Scheme (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0345-2_6

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DOI: 10.1007/978-1-4612-0345-2_6

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