On the automorphism groups of finite multitype models in \(\mathbb C^n\) (Q1725882)

The authors established an explicit description for the automorphism group of a finite multitype (in the sense of Catlin) model in \(\mathbb{C}^n\), which is defined by \[ M_P = \left\{(z_1, \ldots , z_n) \in \mathbb{C}^n \ : \ \operatorname{Re} \, z_n + P(z_1, \ldots , z_{n-1} ) < 0 \right\}, \] where \(P\) is a real-valued weighted homogeneous plurisubharmonic polynomial in \(\mathbb{C}^{n-1}\) without harmonic terms. The finite multitype hypersurface \(\partial M_P\) was defined as a model hypersurface associated to a point of finite Catlin's multitype. See [\textit{D. Catlin}, Ann. Math. (2) 120, 529--586 (1984; Zbl 0583.32048)] and more recently [\textit{M. Kolar}, Int. Math. Res. Not. IMRN, 18, 3530--3548 (2010; Zbl 1207.32032)].