Algebraic approximation in CR geometry Academic Article uri icon

abstract

  • We prove the following CR version of Artin's approximation theorem for holomorphic mappings between real-algebraic sets in complex space. Let . MCN 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'CNCN' and every positive integer . , if . f:(CN,p)CN' is a germ of a holomorphic map such that . Graphf(MCN')S', then there exists a germ of a complex-algebraic map . f:(CN,p)CN' such that . Graphf(MCN')S' and that agrees with . f at . p up to order . . . 2011 Elsevier Masson SAS.

published proceedings

  • Journal de Mathmatiques Pures et Appliques

author list (cited authors)

  • Mir, N.

citation count

  • 4

complete list of authors

  • Mir, Nordine

publication date

  • July 2012