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

Merker, Joël

Bull. Soc. Math. Fr. 129, No. 4, 547-591 (2001).

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.

Reviewer: Mauro Nacinovich (Roma)

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

Keywords:

local holomorphic mappings; real algebraic sets; transcendence degree; local algebraic foliations; Tumanov’s minimality; Segre chains