Le théorème de complexification semi-propre

E. Fortuna; M. Galbiati

Annales de l'institut Fourier (1983)

  • Volume: 33, Issue: 1, page 53-65
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Fortuna, E., and Galbiati, M.. "Le théorème de complexification semi-propre." Annales de l'institut Fourier 33.1 (1983): 53-65. <http://eudml.org/doc/74575>.

@article{Fortuna1983,
abstract = {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.},
author = {Fortuna, E., Galbiati, M.},
journal = {Annales de l'institut Fourier},
keywords = {subanalytic image of real analytic semi-proper map; semi-proper complexification},
language = {fre},
number = {1},
pages = {53-65},
publisher = {Association des Annales de l'Institut Fourier},
title = {Le théorème de complexification semi-propre},
url = {http://eudml.org/doc/74575},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Fortuna, E.
AU - Galbiati, M.
TI - Le théorème de complexification semi-propre
JO - Annales de l'institut Fourier
PY - 1983
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 1
SP - 53
EP - 65
AB - 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.
LA - fre
KW - subanalytic image of real analytic semi-proper map; semi-proper complexification
UR - http://eudml.org/doc/74575
ER -

References

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  1. [1] A. ANDREOTTI, W. STOLL, Analytic and algebraic dependence of meromorphic functions, Lecture notes in Mathematics, vol. 234, Berlin, Heidelberg, New York, Springer, 1971. Zbl0222.32013MR52 #11124
  2. [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. Zbl0325.32002MR54 #7834
  3. [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. Zbl0424.32004
  4. [4] H. HIRONAKA, Subanalytic sets. Dans : Number theory, in honour of Akizuki, Tokyo, Kinokuniya, 1973. Zbl0297.32008MR51 #13275
  5. [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. [6] N. KUHLMANN, Ueber holomorphie Abbildungen komplexer Räume, Arch. Math., 15 (1964), 81-90. Zbl0122.08701MR30 #2165
  7. [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. Zbl0144.08002
  8. [8] N. KUHLMANN, Bemerkungen über holomorphe Abbildungen komplexer Räume. Dans : Festchr. Gedächtnisfeier K. Weierstr., 475-522, Cologne, Westdeutscher Verlag, 1966. Zbl0144.34001

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