Divergence of the normalization for real Lagrangian surfaces near complex tangents

Xianghong Gong

Vol. 176 (1996), No. 2, 311–324

DOI: 10.2140/pjm.1996.176.311

Abstract

We study real Lagrangian analytic surfaces in ℂ² with a non-degenerate complex tangent. Webster proved that all such surfaces can be transformed into a quadratic surface by formal symplectic transformations of ℂ². 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 ℂ². The divergence is contributed by the parabolic character of a pair of involutions generated by the real Lagrangian surfaces.

Mathematical Subject Classification

Primary: 32F25

Milestones

Received: 26 January 1995

Published: 1 December 1996