Algebraic approximation in CR geometry

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We prove the following CR version of Artin's approximation theorem for holomorphic mappings between real-algebraic sets in complex space. Let . M⊂CN be a real-algebraic CR submanifold whose CR orbits are all of the same dimension. Then for every point . p∈. M, for every real-algebraic subset . S'⊂CN×CN' and every positive integer . ℓ, if . f:(CN,p)→CN' is a germ of a holomorphic map such that . Graphf∩(M×CN')⊂S', then there exists a germ of a complex-algebraic map . fℓ:(CN,p)→CN' such that . Graphfℓ∩(M×CN')⊂S' and that agrees with . f at . p up to order . ℓ. .

Original languageEnglish
Pages (from-to)72-88
Number of pages17
JournalJournal des Mathematiques Pures et Appliquees
Issue number1
Publication statusPublished - 1 Jul 2012



  • Algebraic map
  • CR manifold
  • CR orbits

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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