Analytic Continuation of Holomorphic Mappings From Non-minimal Hypersurfaces
- Resource Type
- Working Paper
- Authors
- Kossovskiy, I.; Shafikov, R.
- Source
- Subject
- Mathematics - Complex Variables
32
- Language
We study the analytic continuation problem for a germ of a biholomorphic mapping from a non-minimal real hypersurface $M\subset\CC{n}$ into a real hyperquadric $\mathcal Q\subset\CP{n}$ 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.
Comment: Final version; To appear in "Indiana Journal of Mathematics"