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Germs of holomorphic mappings between real algebraic hypersurfaces. (English) Zbl 0914.32009
A real algebraic hypersurface in \(\mathbb C^n\) is the zero set of a real polynomial with non-vanishing gradient. The following setting is called the general situation: Let \((M,p_0)\) and \((M',p'_0)\) be two germs of real algebraic hypersurfaces in \(\mathbb C^{N+1},N\geqslant 1,\) with \(M\) not Levi-flat, and \(H :\mathbb C^{N+ 1}\to\mathbb C^{N+1}\) a germ at \(p_0\) of a holomorphic map of generic maximal rank (i.e. \(\text{Jac} (H)\not\equiv 0)\) such that \(H(p_0)=p'_0\) and \(H(M)\subseteq M'\). The paper gives an answer to the question: What can be said about the mapping \(H\) without assuming any nondegeneracy condition on the manifolds?

32H99 Holomorphic mappings and correspondences
32D99 Analytic continuation
32D15 Continuation of analytic objects in several complex variables
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