Titlebook: Integrable Systems in the realm of Algebraic Geometry; Pol Vanhaecke Book 19961st edition Springer-Verlag Berlin Heidelberg 1996 abelian v

STIT

原来

Integrable Hamiltonian systems and symmetric products of curves,t equipped with many different Poisson structures: for each non-zero . ∈ C[.] we construct (in Paragraph 2.2) a Poisson bracket {·, ·}. which makes (C., {·, ·}.) into an affine Poisson variety. Each of these brackets has maximal rank 2. (in particular the algebra of Casimirs is trivial) and they are

Infelicity

Interludium: the geometry of Abelian varieties, new in this chapter, our intention was to give a compact and coherent presentation of the theory of Abelian varieties in a form suitable for applications to integrable systems. Our exposition is partly algebraic partly analytic, we think that both approaches highlight different aspects of the theor

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抗原

The master systems,hat they are a.c.i. will be given in Paragraph 4). They are contained in what we called the hyperelliptic case, with a very special choice of Poisson structure (namely the easiest one, which corresponds . = 1) and the underlying space C. should have a dimension which is twice the genus of the hypere

Callus

ARY

Integrable Hamiltonian systems and symmetric products of curves,., {·, ·}.) into an affine Poisson variety. Each of these brackets has maximal rank 2. (in particular the algebra of Casimirs is trivial) and they are all compatible. An explicit formula for all these brackets is given; they grow in complexity (i.e., degree) with . so that only the first members are (modified) Lie-Poisson structures.

PHON

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Licentious