Sur la convexité holomorphe. Théorie locale

A. Fabiano; P. Pietramala

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 3, page 597-617
  • ISSN: 0373-0956

Abstract

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We define a geometric convexity notion for certain open subsets of C n . We prove some results about local cohomology expliciting the topology of the last non zero cohomology group ; the cohomology here considered is the Dolbeault’s cohomology of differential forms.

How to cite

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Fabiano, A., and Pietramala, P.. "Sur la convexité holomorphe. Théorie locale." Annales de l'institut Fourier 40.3 (1990): 597-617. <http://eudml.org/doc/74889>.

@article{Fabiano1990,
abstract = {On définit une notion de convexité géométrique pour des ensembles ouverts de $\{\bf C\}^n$. On démontre des résultats de cohomologie locale précisant la topologie du dernier groupe de cohomologie non nul; la cohomologie considérée ici est la cohomologie de Dolbeault pour les formes différentielles.},
author = {Fabiano, A., Pietramala, P.},
journal = {Annales de l'institut Fourier},
keywords = {geometric convexity; Dolbeault cohomology of differential forms; polyhedra; privileged neighborhoods},
language = {fre},
number = {3},
pages = {597-617},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sur la convexité holomorphe. Théorie locale},
url = {http://eudml.org/doc/74889},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Fabiano, A.
AU - Pietramala, P.
TI - Sur la convexité holomorphe. Théorie locale
JO - Annales de l'institut Fourier
PY - 1990
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 3
SP - 597
EP - 617
AB - On définit une notion de convexité géométrique pour des ensembles ouverts de ${\bf C}^n$. On démontre des résultats de cohomologie locale précisant la topologie du dernier groupe de cohomologie non nul; la cohomologie considérée ici est la cohomologie de Dolbeault pour les formes différentielles.
LA - fre
KW - geometric convexity; Dolbeault cohomology of differential forms; polyhedra; privileged neighborhoods
UR - http://eudml.org/doc/74889
ER -

References

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  1. [1] A. ANDREOTTI et H. GRAUERT, Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France, 90 (1962), 193-259. Zbl0106.05501MR27 #343
  2. [2] A. ANDREOTTI et A. KAS, Duality on complex spaces, Ann. Sc. Norm. Sup. Pisa, 27 (1973), 187-263. Zbl0278.32007MR54 #13117
  3. [3] H. CARTAN, Théorie des fonctions de plusieurs variables, Séminaires E.N.S. 1951-1952, Paris 1952. Zbl0049.06404
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  5. [5] R. GODEMENT, Théorie des faisceaux, Hermann, Paris, 1958. Zbl0080.16201
  6. [6] J.J. KOHN, Boundary Regularity of ∂ in Recent Developments in Several Complex Variables, Princeton University Press, Princeton N.J. 1981, 243-260. Zbl0469.35072
  7. [7] R. NARASIMHAN, The Levi Problem for Complex Spaces, Math. Ann., 142 (1961), 355-365. Zbl0106.28603MR26 #6439
  8. [8] R. NARASIMHAN, The Levi Problem for Complex Spaces II, Math. Ann., 146 (1962), 195-216. Zbl0131.30801MR32 #229
  9. [9] J.P. RAMIS, Théorèmes de séparation et de finitude pour l'homologie et la cohomologie des espaces (p, q)-convexes-concaves, Ann. Sc. Norm. Sup. Pisa, Ser. 3, 27 (1973), 933-997. Zbl0327.32001
  10. [10] R.M. RANGE, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer Verlag, N.Y., 1986. Zbl0591.32002MR87i:32001
  11. [11] H.H. SCHAEFER, Topological Vector Spaces, Mac Millan, N.Y., 1966. Zbl0141.30503MR33 #1689

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