Algebraicity of holomorphic mappings between real algebraic sets in \(\mathbb{C}^ n\)

DOI10.1007/BF02392622zbMath0890.32005arXivmath/9510201MaRDI QIDQ1373010

Linda Preiss Rothschild, Mohamed Salah Baouendi, Peter Ebenfelt

Publication date: 5 November 1997

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9510201

zbMATH Keywords

algebraicity of holomorphic mappingsholomorphic algebraic functionreal algebraic CR manifoldSegre set

Mathematics Subject Classification ID

Real algebraic sets (14P05) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) CR structures, CR operators, and generalizations (32V05) CR manifolds (32V99)

Related Items (33)

Rationality of meromorphic functions between real algebraic sets in the plane ⋮ Projection on Segre varieties and determination of holomorphic mappings between real submanifolds ⋮ Unnamed Item ⋮ A complete normal form for everywhere Levi-degenerate hypersurfaces in \(\mathbb{C}^3\) ⋮ Holomorphic deformations of real-analytic CR maps and analytic regularity of CR mappings ⋮ The finite jet determination problem for CR maps of positive codimension into Nash manifolds ⋮ Automorphism groups of minimal real-analytic CR manifolds ⋮ Reflection ideals and mappings between generic submanifolds in complex space ⋮ Some aspects of holomorphic mappings: a survey ⋮ Regularity of mappings into classical domains ⋮ Algebraic approximation in CR geometry ⋮ Infinitesimal and local rigidity of mappings of CR manifolds ⋮ An example of a real analytic strongly pseudoconvex hypersurface which is not holomorphically equivalent to any algebraic hypersurface ⋮ CR transversality of holomorphic mappings between generic submanifolds in complex spaces ⋮ Extension of holomorphic maps between real hypersurfaces of different dimension ⋮ Reflection principle and boundary properties of holomorphic mappings ⋮ Dynamics of the Segre varieties of a real submanifold in complex space ⋮ Note on double reflection and algebraicity of holomorphic mappings ⋮ A removable singularity property for cr mappings between real analytic hypersurfaces ⋮ Determination of formal CR mappings by a finite jet ⋮ Formal versus analytic CR mappings ⋮ Analytic Jet Parametrization for CR Automorphisms of Some Essentially Finite CR Manifolds ⋮ Unique jet determination and extension of germs of CR maps into spheres ⋮ Germs of holomorphic mappings between real algebraic hypersurfaces ⋮ Parametrization of local CR automorphisms by finite jets and applications ⋮ Two decades of finite jet determination of CR mappings ⋮ Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spaces ⋮ Convergence and finite determination of formal CR mappings ⋮ Extension of CR maps between real-analytic hypersurfaces of different dimensions ⋮ Approximation and convergence properties of formal CR-maps ⋮ On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle ⋮ Algebraicity of real analytic hypersurfaces and blowing-down. ⋮ Study of the analytic regularity of formal CR reflection mappings

Cites Work

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