5. Normal Forms

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 nondegenerate hypersurfaces there is the ChernMoser 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: CauchyRiemann equations in several variables, available at http://aimpl.org/crscv.