Cauchy-Riemann automorphism groups that cannot be projectively realized (Q1203496)

Let \(M\subset\mathbb{C}^ n\), \(n\geq 2\) be a real-analytic, nonspherical hypersurface with nondegenerate Levi-form passing through the origin and let \(\text{Aut}_ 0M\) be its stability group. The author constructs an example of a hypersurface \(M\subset\mathbb{C}^{12}\) such that there are no local coordinates in \((\mathbb{C}^{12},0)\) in which all the elements of \(\text{Aut}_ 0M\) can be written as fractional linear transformations.