Transcendental holomorphic maps between real algebraic manifolds in a complex space
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- by Guillaume Rond PDF
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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.References
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Additional Information
- Guillaume Rond
- Affiliation: Aix-Marseille Université, LASOL, UMI2001, UNAM, Mexico
- MR Author ID: 759916
- Email: guillaume.rond@univ-amu.fr
- Received by editor(s): May 21, 2019
- Received by editor(s) in revised form: September 2, 2019, and September 17, 2019
- Published electronically: January 15, 2020
- Additional Notes: The author is deeply grateful to the UMI LASOL of the CNRS where this project has been carried out.
- Communicated by: Harold P. Boas
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 2097-2102
- MSC (2010): Primary 32H02; Secondary 05A15, 14P05, 32C05, 32V40, 39B32
- DOI: https://doi.org/10.1090/proc/14865
- MathSciNet review: 4078093