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 hy- persurface M ⊂ C n into a real hyperquadric Q ⊂ CP n , 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 ⊃ X. Using the monodromy representation for the multiple-valued mapping obtained by the analytic continuation, we establish a connection between nonminimal real hypersurfaces and singu- lar complex ODEs.