A classification of non-degenerate homogeneous equiaffine hypersurfaces in four complex dimensions
An equiaffine transformation of \(\mathbb{C}^n\) is a map of type \(V \mapsto Av+b\), where \(A\in SL(h,\mathbb{C})\) and \(b\in\mathbb{C}^n\). An equiaffine homogeneous hypersurface of \(\mathbb{C}^n\) is a complex hypersurface \(\Sigma\subset \mathbb{C}^n\) which is the orbit of a complex Lie subgroup of the group of all equiaffine transformations. Such surfaces in \(\mathbb{C}^3\) were classified by \textit{K. Nomizu} and \textit{T. Sasaki} in [Manuscr. Math. 73, 39-44 (1991; Zbl 0753.53008)]. In the paper under review, the corresponding classification problem is solved for non-degenerate hypersurfaces of \(\mathbb{C}^n\). These hypersurfaces are explicitly described via equations and computable invariants are found which distinguish between different non-equivalent hypersurfaces.
scientific article; zbMATH DE number 1818551