Quasi-homogénéité des applications holomorphes propres d’un domaine quasi-disqué sur un domaine disqué
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 4, p. 759-765

A result of F. Berteloot and G.Patrizio [1] states that if f is a proper holomorphic map between two bounded complete circular domains Ω 1 and Ω 2 in C n+1 (n1), such that f -1 {0}={0} and such that the principal part f p of the Taylor expansions of f at the origin is nondegenerated i.e f p -1 {0}={0}, then ff p . Here we propose to generalize their result in the case where Ω 1 is a complete quasi-circular domain and Ω 2 is a complete circular domain. Moreover this proof does not use the tools of projective dynamics of J. E. Fornaess and N. Sibony [3].

Nous proposons une généralisation d’un résultat de F. Berteloot et G. Patrizio [1], aux cas des applications holomorphes propres entre domaines quasi-disqués et non nécessairement bornés.

@article{AFST_2011_6_20_4_759_0,
     author = {Boutat, Moha},
     title = {Quasi-homog\'en\'eit\'e des applications holomorphes propres d'un domaine quasi-disqu\'e sur un domaine disqu\'e},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {6e s{\'e}rie, 20},
     number = {4},
     year = {2011},
     pages = {759-765},
     doi = {10.5802/afst.1322},
     mrnumber = {2918212},
     zbl = {1243.32014},
     language = {fr},
     url = {http://www.numdam.org/item/AFST_2011_6_20_4_759_0}
}
Boutat, Moha. Quasi-homogénéité des applications holomorphes propres d’un domaine quasi-disqué sur un domaine disqué. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 4, pp. 759-765. doi : 10.5802/afst.1322. http://www.numdam.org/item/AFST_2011_6_20_4_759_0/

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