Previous |  Up |  Next


Title: Grauert's line bundle convexity, reduction and Riemann domains (English)
Author: Vâjâitu, Viorel
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 66
Issue: 2
Year: 2016
Pages: 493-509
Summary lang: English
Category: math
Summary: We consider a convexity notion for complex spaces $X$ with respect to a holomorphic line bundle $L$ over $X$. This definition has been introduced by Grauert and, when $L$ is analytically trivial, we recover the standard holomorphic convexity. In this circle of ideas, we prove the counterpart of the classical Remmert's reduction result for holomorphically convex spaces. In the same vein, we show that if $H^0(X,L)$ separates each point of $X$, then $X$ can be realized as a Riemann domain over the complex projective space $\Bbb {P}^n$, where $n$ is the complex dimension of $X$ and $L$ is the pull-back of ${\mathcal O}(1)$. (English)
Keyword: Grauert's line bundle convexity
Keyword: Riemann domain
Keyword: holomorphic reduction
MSC: 32E05
MSC: 32E99
MSC: 32F17
idZBL: Zbl 06604482
idMR: MR3519617
DOI: 10.1007/s10587-016-0271-0
Date available: 2016-06-16T12:58:38Z
Last updated: 2020-07-03
Stable URL:
Reference: [1] Andreotti, A.: Théorèmes de dépendance algébrique sur les espaces complexes pseudo-concaves.Bull. Soc. Math. Fr. 91 (1963), 1-38 French. Zbl 0113.06403, MR 0152674
Reference: [2] Stănăşilă, C. Bănică; O.: Méthodes Algébriques dans la Théorie Globale des Espaces Complexes. Vol. 2. Traduit du Roumain.Collection ``Varia Mathematica'' Gauthier-Villars, Paris (1977), French. MR 0508024
Reference: [3] Silva, D. Barlet; A.: Convexité holomorphe intermédiaire.Math. Ann. 296 (1993), 649-665 French. English summary. MR 1233489, 10.1007/BF01445127
Reference: [4] Cartan, H.: Quotients of complex analytic spaces.Contrib. Function Theory Int. Colloqu. Bombay, 1960 Tata Institute of Fundamental Research, Bombay (1960), 1-15. Zbl 0154.33603, MR 0139769
Reference: [5] Grauert, H.: Bemerkenswerte pseudokonvexe Mannigfaltigkeiten.Math. Z. 81 (1963), 377-391 German. Zbl 0151.09702, MR 0168798
Reference: [6] Grauert, H.: Charakterisierung der holomorph vollständigen komplexen Räume.Math. Ann. 129 (1955), 233-259 German. Zbl 0064.32603, MR 0071084, 10.1007/BF01362369
Reference: [7] Kaup, B.: Über offene analytische "{A}quivalenzrelationen auf komplexen Räumen.Math. Ann. 183 (1969), 6-16 German. MR 0248348, 10.1007/BF01361259
Reference: [8] Remmert, R.: Sur les espaces analytiques holomorphiquement séparables et holomorphiquement convexes.C. R. Acad. Sci., Paris 243 (1956), 118-121 French. Zbl 0070.30401, MR 0079808
Reference: [9] Shiffman, B.: On the removal of singularities for analytic sets.Mich. Math. J. 15 (1968), 111-120. MR 0224865, 10.1307/mmj/1028999912
Reference: [10] Siu, Y.-T.: Techniques of Extension of Analytic Objects.Lecture Notes in Pure and Applied Mathematics, Vol. 8 Marcel Dekker, New York (1974). Zbl 0294.32007, MR 0361154
Reference: [11] Ueda, T.: On the neighborhood of a compact complex curve with topologically trivial normal bundle.J. Math. Kyoto Univ. 22 (1983), 583-607. Zbl 0519.32019, MR 0685520, 10.1215/kjm/1250521670


Files Size Format View
CzechMathJ_66-2016-2_16.pdf 325.0Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo