Analytic Continuation of Holomorphic Mappings From Non-minimal Hypersurfaces

Details Analytic Continuation of Holomorphic Mappings From Non-minimal Hypersurfaces Analytic Continuation of Holomorphic Mappings From Non-minimal Hypersurfaces

2012-03-16

arxiv.org/abs/1203.3829v2

Mathematics

Complex Variables

Scientific paper

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.

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