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On the partial algebraicity of holomorphic mappings between two real algebraic sets. (English) Zbl 0998.32019

The author discusses classical and more recent results about the algebraicity of holomorphic mappings between real algebraic sets, by building a study of the transcendence degree of such mappings. He also discusses the meaning of Tumanov’s minimality condition in arbitrary dimension and without any assumption on the rank, for arbitrary real algebraic sets.

MSC:

32V25 Extension of functions and other analytic objects from CR manifolds
32V40 Real submanifolds in complex manifolds
32V15 CR manifolds as boundaries of domains
32V10 CR functions
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