An algebraic characterization of holomorphic nondegeneracy for real algebraic hypersurfaces and its application to CR mappings (Q1297974)

We give a new algebraic characterization of holomorphic nondegeneracy for embedded real algebraic hypersurfaces in \(\mathbb{C}^{N+1}\), \(N\geq 1\). We then use this criterion to prove the following result about real analyticity of smooth CR mappings: any smooth CR mapping \(H\) between a real analytic hypersurface and a rigid polynomial holomorphically nondegenerate hypersurface is real analytic, provided the map \(H\) is not totally degenerate in the sense of Baouendi and Rothschild.