Note on double reflection and algebraicity of holomorphic mappings

Joel Merker (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

In this note, we provide the corrections to an article by D. Zaitsev, Acta Math., 183 (1999), 273-305. Building on a remark by S. Damour, we provide twenty counterexamples to the preprint version of the mentioned reference. Our main purpose is to establish shortly the algebraicity of a holomorphic mapping between real algebraic CR manifolds under a double reflection condition which generalizes the classical single reflection. A complete study of various double reflection conditions is also provided

Mots clés: algebraicity; reflection principle; double reflection; reduction of the first characteristic variety; tree of counterexamples; Holomorphic mappings

Domaines: Géométrie différentielle [math.DG]; Variables complexes [math.CV]

Joel Merker. Note on double reflection and algebraicity of holomorphic mappings. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2000, 9, pp.no.4, 689-721. ⟨hal-00003376⟩