IUMJ

Title: Analytic Continuation of Holomorphic Mappings from Nonminimal Hypersurfaces

Authors: Ilya Kossovskiy and Rasul Shafikov

Issue: Volume 62 (2013), Issue 6, 1891-1916

Abstract:

We study the analytic continuation problem for a germ of a biholomorphic mapping from a nonminimal real hypersurface $M\subset\mathbb{C}^n$ into a real hyperquadric $\mathcal{Q}\subset\mathbb{CP}^n$, and we prove that, under certain nondegeneracy 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 neighbourhood $U\supset X$. 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.