Extension of CR mappings between generic algebraic submanifolds
The Author extends to the case of germs of connected algebraic generic CR submanifolds of \(\mathbb{C}^n\) of any codimension a result originally proved by \textit{M. S. Baouendi, X. Huang} and \textit{L. Rothschild} [Invent. Math. 125, No.1, 13--36 (1996; Zbl 0855.32009)] for the hypersurface case. He shows that a (germ of) CR map \(f:(M,o)\to(M',o')\), with a nonsingular Jacobian from an \(M\subset\mathbb{C}^n\) which is generic, holomorphically nondegenerate, and has a point of finite type, to an \(M'\subset\mathbb{C}^n\) of the same CR dimension and codimension holomorphically extends as a biholomorphism in a full complex neighborhood of \(o\) in \(\mathbb{C}^n\).
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