On the partial algebraicity of holomorphic mappings between two real algebraic sets  [ Algébricité partielle des applications holomorphes entre deux ensembles algébriques réels ]
Bulletin de la Société Mathématique de France, Tome 129 (2001) no. 4, p. 547-591
La rigidité des invariants locaux des structures de Cauchy-Riemann réelles algébriques impose aux applications holomorphes des propriétés globales de rationalité (Poincaré 1907), ou plus généralement d'algébricité (Webster 1977). Notre objectif principal sera d'unifier les résultats classiques ou récents, grâce à une étude du degré de transcendance, de discuter aussi l'hypothèse habituelle de minimalité au sens de Tumanov, et ce en dimension quelconque, sans hypothèse de rang et pour des applications holomorphes quelconques entre deux ensembles algébriques réels arbitraires.
The rigidity properties of the local invariants of real algebraic Cauchy-Riemann structures imposes upon holomorphic mappings some global rational properties (Poincaré 1907) or more generally algebraic ones (Webster 1977). Our principal goal will be to unify the classical or recent results in the subject, building on a study of the transcendence degree, to discuss also the usual assumption of minimality in the sense of Tumanov, in arbitrary dimension, without rank assumption and for holomorphic mappings between two arbitrary real algebraic sets.
DOI : https://doi.org/10.24033/bsmf.2408
Classification:  32V25,  32V40,  32V15,  32V10
@article{BSMF_2001__129_4_547_0,
     author = {Merker, Jo\"el},
     title = {On the partial algebraicity of holomorphic mappings between two real algebraic sets},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {129},
     number = {4},
     year = {2001},
     pages = {547-591},
     doi = {10.24033/bsmf.2408},
     zbl = {0998.32019},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2001__129_4_547_0}
}
Merker, Joël. On the partial algebraicity of holomorphic mappings between two real algebraic sets. Bulletin de la Société Mathématique de France, Tome 129 (2001) no. 4, pp. 547-591. doi : 10.24033/bsmf.2408. http://www.numdam.org/item/BSMF_2001__129_4_547_0/

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