Transcendental holomorphic maps between real algebraic manifolds in a complex space - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2020

Transcendental holomorphic maps between real algebraic manifolds in a complex space

Guillaume Rond

Résumé

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.

Dates et versions

hal-03455235 , version 1 (29-11-2021)

Identifiants

Citer

Guillaume Rond. Transcendental holomorphic maps between real algebraic manifolds in a complex space. Proceedings of the American Mathematical Society, 2020, 148 (5), pp.2097-2102. ⟨10.1090/proc/14865⟩. ⟨hal-03455235⟩
6 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More