Divergence of the normalization for real Lagrangian surfaces near complex tangents

Details Divergence of the normalization for real Lagrangian surfaces near complex tangents Divergence of the normalization for real Lagrangian surfaces near complex tangents

1995-06-29

arxiv.org/abs/math/9506202v1

Mathematics

Complex Variables

Scientific paper

We study real Lagrangian analytic surfaces in C^2 with a non-degenerate complex tangent. Webster proved that all such surfaces can be transformed into a quadratic surface by formal symplectic transformations of C^2. We show that there is a certain dense set of real Lagrangian surfaces which cannot be transformed into the quadratic surface by any holomorphic (convergent) transformation of C^2. The divergence is contributed by the parabolic character of a pair of involutions generated by the real Lagrangian surfaces.

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