Analytic Continuation of Holomorphic Mappings from Nonminimal Hypersurfaces

Abstract

We study the analytic continuation problem for a germ of a biholomorphic mapping from a nonminimal real hypersurface M ⊂ C n into a real hyperquadric Q ⊂ CP n and 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 ⊃ 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.