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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?

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