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

摘要

We give a new algebraic characterization of holomorphic nondegeneracy for embedded real algebraic hypersurfaces in C~(N+1) , N >= 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 hyper-surface is real analytic, provided the map H is not totally degenerate in the sense of Baouendi and Rothschild.