Germs of CR maps between real analytic hypersurfaces. (English) Zbl 0653.32020

Baouendi, M. S.; Rothschild, Linda Preiss

Invent. Math. 93, No. 3, 481-500 (1988).

Suppose H is a smooth CR mapping between two real-analytic hypersurfaces M and M’ in \({\mathbb{C}}^{n+1}\) and let \(P_ 0\in M\). The authors derive sufficient conditions for H to extend holomorphically to an ambient neighborhood of \(P_ 0\). The conditions are given in terms of algebraic concepts, essential finiteness of M at \(P_ 0\) and M’ at \(H(p_ 0)\), and finite multiplicity of H at \(P_ 0\). The techniques are rather algebraic as well, using such results as Nakayama’s Lemma, the Nullstellensatz, and the Weierstrass Preparation Theorem.

Reviewer: G.Harris

MSC:

32V40

Real submanifolds in complex manifolds

Keywords:

CR mapping; real-analytic hypersurfaces; essential finiteness; finite multiplicity

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