Analytic Continuation of Holomorphic Mappings from Non minimal Hypersurfaces

We study the analytic continuation problem for a germ of a biholomorphic mapping from a nonminimal real hypersurface M subset of C-n into a real hyperquadric Q subset of CPn, and we prove that, under certain nondegeneracy conditions, any such germ extends locally biholomorphically along any path lying in the complement U \ X of the complex hypersurface X contained in M for an appropriate neighbourhood U superset of 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.