Une nouvelle version du théorème d'extension de Hartogs pour les applications séparément holomorphes entre espaces analytiques

O. Alehyane; A. Zeriahi

Annales Polonici Mathematici (2001)

  • Volume: 76, Issue: 3, page 245-278
  • ISSN: 0066-2216

Abstract

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This paper is concerned with the problem of extension of separately holomorphic mappings defined on a "generalized cross" of a product of complex analytic spaces with values in a complex analytic space. The crosses considered here are inscribed in Borel rectangles (of a product of two complex analytic spaces) which are not necessarily open but are non-pluripolar and can be quite small from the topological point of view. Our first main result says that the singular set of a given separately holomorphic mapping defined on such a cross is quite small from the pluripotential point of view in the product space in the sense that each of its projections is pluripolar. Then for some special crosses, we deduce more precise results on the extension of separately holomorphic mappings on such crosses, giving generalizations of all the main results obtained earlier by various authors in this direction.

How to cite

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O. Alehyane, and A. Zeriahi. "Une nouvelle version du théorème d'extension de Hartogs pour les applications séparément holomorphes entre espaces analytiques." Annales Polonici Mathematici 76.3 (2001): 245-278. <http://eudml.org/doc/281099>.

@article{O2001,
author = {O. Alehyane, A. Zeriahi},
journal = {Annales Polonici Mathematici},
keywords = {separately holomorphic mapping; pluripolar set; Hartogs theorem},
language = {fre},
number = {3},
pages = {245-278},
title = {Une nouvelle version du théorème d'extension de Hartogs pour les applications séparément holomorphes entre espaces analytiques},
url = {http://eudml.org/doc/281099},
volume = {76},
year = {2001},
}

TY - JOUR
AU - O. Alehyane
AU - A. Zeriahi
TI - Une nouvelle version du théorème d'extension de Hartogs pour les applications séparément holomorphes entre espaces analytiques
JO - Annales Polonici Mathematici
PY - 2001
VL - 76
IS - 3
SP - 245
EP - 278
LA - fre
KW - separately holomorphic mapping; pluripolar set; Hartogs theorem
UR - http://eudml.org/doc/281099
ER -

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