Le théorème de complexification semi-propre
Fortuna, E. ; Galbiati, M.
Annales de l'Institut Fourier, Tome 33 (1983), p. 53-65 / Harvested from Numdam
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Il est bien connu que l’image d’une application analytique complexe semi-propre est un ensemble analytique; dans le cas réel elle est en général sous-analytique. Dans cet article on donne des conditions pour la semi-analyticité de l’image d’une application analytique réelle, semi-propre qui admet une complexification semi-propre.

It is well-known that the image of a complex analytic semi-proper map is an analytic set; in the real case, the image is in general subanalytic. In this paper we find a condition for the semi-analyticity of the image of a real analytic semi-proper map which has a semi-proper complexification.

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     author = {Fortuna, E. and Galbiati, M.},
     title = {Le th\'eor\`eme de complexification semi-propre},
     journal = {Annales de l'Institut Fourier},
     volume = {33},
     year = {1983},
     pages = {53-65},
     doi = {10.5802/aif.904},
     mrnumber = {84g:32010},
     zbl = {0487.32003},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1983__33_1_53_0}
}

Fortuna, E.; Galbiati, M. Le théorème de complexification semi-propre. Annales de l'Institut Fourier, Tome 33 (1983) pp. 53-65. doi : 10.5802/aif.904. http://gdmltest.u-ga.fr/item/AIF_1983__33_1_53_0/

[1] A. Andreotti, W. Stoll, Analytic and algebraic dependence of meromorphic functions, Lecture notes in Mathematics, vol. 234, Berlin, Heidelberg, New York, Springer, 1971. | MR 52 #11124 | Zbl 0222.32013

[2] M. Galbiati, Sur l'image d'un morphisme analytique réel propre, Ann. Scuola Norm. Sup. Pisa, Cl. Sci., Serie IV, vol. III (1976), 311-319. | Numdam | MR 54 #7834 | Zbl 0325.32002

[3] H. Hironaka, Stratification and flatness. Dans : Real and Complex Singularities, Nordic Summer School Oslo 1976, 199-265, Alphen aan den Rijn, Sijthoff & Noordhoff 1977. | Zbl 0424.32004

[4] H. Hironaka, Subanalytic sets. Dans : Number theory, in honour of Akizuki, Tokyo, Kinokuniya, 1973. | MR 51 #13275 | Zbl 0297.32008

[5] H. Hironaka, Introduction to real analytic sets and real analytic maps, Quaderno dei gruppi di ricerca del C.N.R., Pisa, Istituto Mat. "L. Tonelli", 1973.

[6] N. Kuhlmann, Ueber holomorphie Abbildungen komplexer Räume, Arch. Math., 15 (1964), 81-90. | MR 30 #2165 | Zbl 0122.08701

[7] N. Kuhlmann, Algebraic function fields on complex analytic spaces. Dans : Proc. Conf. on Compl. Anal. Minneapolis, 1964, 155-172. Berlin, Heidelberg, New York, Springer, 1965. | Zbl 0144.08002

[8] N. Kuhlmann, Bemerkungen über holomorphe Abbildungen komplexer Räume. Dans : Festchr. Gedächtnisfeier K. Weierstr., 475-522, Cologne, Westdeutscher Verlag, 1966. | Zbl 0144.34001