2002/05/14 by Francine Meylan, Meylan, Francine, Nordine Mir +3
Mathematics · #32H02 #32V20 #32V40 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.AG #math.CV #msc:32H02 #msc:32V20 #msc:32V40
paper · pdf · doi:10.48550/arxiv.math/0205151
arxiv created 2002/05/14 · openalex publication_date 2002/05/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M⊂ CN be a minimal real-analytic CR-submanifold and M'⊂ CN' a real-algebraic subset through points p∈ M and p'∈ M'. We show that that any formal (holomorphic) mapping f\colon (CN,p)→ (CN',p'), sending M into M', can be approximated up to any given order at p by a convergent map sending M into M'. If M is furthermore generic, we also show that any such map f, that is not convergent, must send (in an appropriate sense) M into the set E'⊂ M' of points of D'Angelo infinite type. Therefore, if M' does not contain any nontrivial complex-analytic subvariety through p', any formal map f as above is necessarily convergent.