## 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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### References:

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