Geodesic
An~estimate of the dimension of the image under a~holomorphic mapping of real-analytic hypersurfaces
Izvestiya. Mathematics , Tome 30 (1988) no. 1, pp. 89-102

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It is shown that if a holomorphic mapping between two real-analytic hypersurfaces in $\mathbf C^n$ with nondegenerate Levi form has zero Jacobian at some point of the first hypersurface, then the Jacobian is identically zero and the mapping takes some open set in $\mathbf C^n$ into the second surface. An estimate is given for the rank of the mapping, depending on the signature of the Levi form of the second surface. Bibliography: 3 titles. 
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     title = {An~estimate of the dimension of the image under a~holomorphic mapping of real-analytic hypersurfaces},
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A. V. Isaev. An~estimate of the dimension of the image under a~holomorphic mapping of real-analytic hypersurfaces. Izvestiya. Mathematics , Tome 30 (1988) no. 1, pp. 89-102. http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a4/