Analytic Continuation of Holomorphic Mappings From Non-minimal Hypersurfaces

We study the analytic continuation problem for a germ of a biholomorphic mapping from a non-minimal real hypersurface $M\subset \text{CC}n$ into a real hyperquadric $\mathcal{Q}\subset \text{CP}n$ and prove that under certain non-degeneracy conditions any such germ extends locally biholomorphically along any path lying in the complement $U\setminus X$ of the complex hypersurface $X$ contained in $M$ for an appropriate neighborhood $U\supset X$. Using the monodromy representation for the multiple-valued mapping obtained by the analytic continuation we establish a connection between nonminimal real hypersurfaces and singular complex ODEs.