Most real analytic Cauchy-Riemann manifolds are nonalgebraizable

2004/06/30 by Franc Forstnerič, Franc Forstneric · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Holomorphic and Operator Theory #math.CV #msc:32V20 #msc:32V30

paper · pdf · doi:10.1007/s00229-004-0507-4

published as Manuscripta math., 115 (2004), 489-494 · To appear in Manuscripta Math

arxiv created 2004/10/07 · openalex publication_date 2004/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We give a very simple argument to the effect that most germs of generic real analytic Cauchy-Riemann manifolds of positive CR dimension are not holomorphically embeddable into any generic real algebraic CR manifold of the same real codimension in a finite dimensional space. In particular, most such germs are not holomorphically equivalent to a germ of a generic real algebraic CR manifold.

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