English

Divergence of the normalization for real Lagrangian surfaces near complex tangents

Complex Variables 2009-09-25 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/9506202,
  title  = {Divergence of the normalization for real Lagrangian surfaces near complex tangents},
  author = {Xianghong Gong},
  journal= {arXiv preprint arXiv:math/9506202},
  year   = {2009}
}