An estimate of the dimension of the image under a holomorphic mapping of real-analytic hypersurfaces

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.
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