On the levi problem with singularities
DOI:
https://doi.org/10.4067/S0716-09172001000100006Abstract
In section 1, we show that if X is a Stein normal complex space of dimension n and D ?? X an open subset which is the union of an increasing sequence D1 ? D2 ? ... ? Dn ?? ... of domains of holomorphy in X, then D is a domain of holomorphy. In section 2, we prove that a domain of holomorphy D which is relatively compact in a 2-dimensional normal Stein space X itself is Stein. In section 3, we show that if X is a Stein space of dimension n and D ? X an open subspace which is the union of an increasing sequence D1 ? D2 ? ... ? Dn ? ... of open Stein subsets of X, then D itself is Stein, if X has isolated singularities.References
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[2] . Behnke.H,Stein,K.: Konvergente Folgen Von Regularitatsbereichen and die Meromorphiekonvexitat, Math. Ann. 166, pp. 204-216, (1938)
[3] . M. Coltoiu,Remarques sur les réunions croissantes d’ouverts de Stein C. R. Acad. Sci. Paris. t. 307, Série I, pp. 91-94, (1988).
[4] . M. Coltoiu, Open problems concerning Stein spaces. Revue Roumaine de Mathématiques Pures et Appliquées.
[5] . Demailly, J. P.: Cohomology of q-convex spaces in top degrees. Math. Z 204, pp. 283-295, (1990).
[6] . Diederich, H., Fornaess, J. E.: Smoothing q-convex functions in the singular case. Math. Ann. 273, pp. 665-671, (1986).
[7] . Fornaess, J. E.: An increasing sequence of Stein manifolds whose limit is not Stein, Math. Ann.223, pp. 275-277, (1976).
[8] . Fornaess J. E., Narasimhan. R.: The levi problem on complex spaces with singularities. Math. Ann. 248, pp. 47-72, (1980).
[9] . Grauert, H., Remmert, R.: Singularitaten Komplexer Manngifaltigkeiten und Riemannsche Gebiete. Math. Z. 67, pp. 103-128, (1957).
[10] . Markoe, A.: Runge Families and Inductive limits of Stein spaces.Ann. Inst. Fourier 27, Fax. 3 (1977).
[11] . Narasimhan, R.: A note on Stein spaces and their normalizations. Ann Scuela Norm. Sup. Pisa 16, pp. 327-333, (1962).
[12] . Peternell, M.: Continuous q-convex exhaustion functions. Invent. Math. 85, pp. 246-263, (1986).
[13] . Stein,K.: Uberlagerungen holomorph-vollstandiger Komplexer Raume.Arch.Math. 7, pp. 354-361, (1956).
[14] . Skoda,H.:Application de techniques L 2 la théorie des idéaux d’une algébre de fonctions holomorphes avec poids. Ann.Sci.Ecole Norm.Sup. Paris 5, pp. 545-579, (1972).
[15] . Simha,R.: On the complement of a curve on a Stein space. Math. Z. 82, pp. 63-66, (1963).
Published
2017-04-24
How to Cite
[1]
A. Youssef, “On the levi problem with singularities”, Proyecciones (Antofagasta, On line), vol. 20, no. 1, pp. 83-91, Apr. 2017.
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