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5. Normal Forms

    1. Problem 5.1.

      [Zaitsev] Let $C$ be a class of hypersurfaces defined by a finite order condition. A normal form is a subclass $C_0$ where normal representatives are determined up to a finite dimensional group. For example, for Levi non-degenerate hypersurfaces there is the Chern-Moser normal form and for finite type hypersurfaces in $\mathbb{C}^2$ Kollar presented a normal form. Can you find a class where it can be proved that there is no convergent normal form?

          Cite this as: AimPL: Cauchy-Riemann equations in several variables, available at http://aimpl.org/crscv.