Transcendental holomorphic maps between real algebraic manifolds in a\n complex space

2019/05/15 by Guillaume Rond, Rond, Guillaume
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1905.06222

openalex publication_date 2019/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an example of a real algebraic manifold embedded in a complex space\nthat does not satisfy the Nash-Artin approximation Property. This Nash-Artin\napproximation Property is closely related to the problem of determining when\nthe biholomorphic equivalence for germs of real algebraic manifolds coincides\nwith the algebraic equivalence. This example is an elliptic Bishop surface, and\nits construction is based on the functional equation satisfied by the\ngenerating series of some walks restricted to the quarter plane.\n

Citations

• Equivalence of Cauchy-Riemann manifolds and multisummability theory

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