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An algebraic characterization of holomorphic nondegeneracy for real algebraic hypersurfaces and its application to CR mappings. (English) Zbl 0930.32020
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.

MSC:
32V40 Real submanifolds in complex manifolds
32H40 Boundary regularity of mappings in several complex variables
32J99 Compact analytic spaces
32V99 CR manifolds
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