Transcendental holomorphic maps between real algebraic manifolds in a complex space

Authors :: Guillaume Rond
Institut de Mathématiques de Marseille (I2M)
Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU)
Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)
Source :: Proceedings of the American Mathematical Society, Proceedings of the American Mathematical Society, American Mathematical Society, 2020, 148 (5), pp.2097-2102. ⟨10.1090/proc/14865⟩, Proceedings of the American Mathematical Society, 2020, 148 (5), pp.2097-2102. ⟨10.1090/proc/14865⟩
Publication Year :: 2020
Publisher :: HAL CCSD, 2020.
Abstract: We give an example of a real algebraic manifold embedded in a complex space that does not satisfy the Nash-Artin approximation Property. This Nash-Artin approximation Property is closely related to the problem of determining when the biholomorphic equivalence for germs of real algebraic manifolds coincides with the algebraic equivalence. This example is an elliptic Bishop surface, and its construction is based on the functional equation satisfied by the generating series of some walks restricted to the quarter plane.<br />to appear in Proceedings of the A.M.S

Language :: English
ISSN :: 00029939 and 10886826
Database :: OpenAIRE
Journal :: Proceedings of the American Mathematical Society, Proceedings of the American Mathematical Society, American Mathematical Society, 2020, 148 (5), pp.2097-2102. ⟨10.1090/proc/14865⟩, Proceedings of the American Mathematical Society, 2020, 148 (5), pp.2097-2102. ⟨10.1090/proc/14865⟩
Accession number :: edsair.doi.dedup.....142b8dd629874cd623bbe6299fb0137a
Full Text :: https://doi.org/10.1090/proc/14865⟩

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