Displaying similar documents to “Holomorphic symplectic normalization of a real function”

Levi-flat invariant sets of holomorphic symplectic mappings

Xianghong Gong (2001)

Annales de l’institut Fourier

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We classify four families of Levi-flat sets which are defined by quadratic polynomials and invariant under certain linear holomorphic symplectic maps. The normalization of Levi- flat real analytic sets is studied through the technique of Segre varieties. The main purpose of this paper is to apply the Levi-flat sets to the study of convergence of Birkhoff's normalization for holomorphic symplectic maps. We also establish some relationships between Levi-flat invariant...

Symplectic subvarieties of projective fibrations over symplectic manifolds

Roberto Paoletti (1999)

Annales de l'institut Fourier

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Given a symplectic fibration E → M , with M compact and symplectic and the fibres complex projective, we produce symplectic submanifolds of E analytic in the vertical direction, and apply this to complex vector bundles on symplectic manifolds.

Invariant properties of the generalized canonical mappings

Stanisław Janeczko (1999)

Banach Center Publications

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One of the fundamental objectives of the theory of symplectic singularities is to study the symplectic invariants appearing in various geometrical contexts. In the paper we generalize the symplectic cohomological invariant to the class of generalized canonical mappings. We analyze the global structure of Lagrangian Grassmannian in the product symplectic space and describe the local properties of generic symplectic relations.