Space of orbits of the automorphism group of a model surface of type (1,2) (Q1033771)

The \(CR\) automorphisms of a model \(CR\) manifold act on the ambient complex space as a group of birational transformations. In the special example of the \(CR\) cubic \[ M=\{\Im z_2=|z_1|^2,\; \Im z_3=2|z_1|^2\Re z_1\}\subset\mathbb{C}^3, \] the author gives a full description of the space of the orbits of the relative group \(\mathbf{G}(M)\) in \(\mathbb{C}^3\).