The normal form of germs of four-dimensional real submanifolds in \(\mathbb{C}^5\) at generic \(\mathbb{R}\mathbb{C}\)-singular points (Q1274072)

The interest of \(RC\)-singular points of a closed real smooth oriented \(m\)-dimensional submanifold \(M\) of \(\mathbb{C}^n\) increases after the papers of H. T. Lai, A. V. Dornrin, J. K. Moser and S. M. Vebster (see the references of the paper). In fact, the problem is to characterize the germ of a surface at an \(RC\)-singular point. With the help of the normal form of the equation of the surface, Moser and Vebster discovered a rich system of holomorphic nonequivalent invariants of such germs in the case \(m=n=2\). Surprisingly, there are no biholomorphic invariants in the case \(n=5\), \(m=4\), and the equation of any generic germ at an \(RC\)-singular point can be reduced to a unique normal form. This is the main result of the author in this paper.