×

zbMATH — the first resource for mathematics

Completeness of noncompact analytic spaces. (English) Zbl 0568.32008
Let X be a (paracompact) complex space of dimension n. The main result of this paper says that X is n-complete if X has no compact branch.

MSC:
32F10 \(q\)-convexity, \(q\)-concavity
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Andreotti, A. and Grauert, H., Theoreme de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193-259. · Zbl 0106.05501 · numdam:BSMF_1962__90__193_0 · eudml:87019
[2] Barlet, D., Espace analytique reduit des cycles analytiques complexes compacts d’un espace analytique complexe de dimension finite, Fonctions de plusieurs variables complexes, II, Seminaire Francois Norguet, 1974/75, p-1-158, Berlin, Springer-Verlag, 1975 (Lecture Notes in Mathematics, 482) (These Sc. math. Universite Paris VII, 1975). · Zbl 0331.32008
[3] , Convexite de 1’espace de cycles, Bull. Soc. math. France, 106 (1978), 373-397.
[4] Greene, R. E. and Wu, H., Embedding of open Riemannian Manifolds by harmonic functions, Ann. Inst. Fourier, Grenoble 25, 1 (1975), 215-235. · Zbl 0307.31003 · doi:10.5802/aif.549 · numdam:AIF_1975__25_1_215_0 · eudml:74211
[5] Komatsu, H., Resolutions by hyperfunctions of sheaves of solutions of differential equa- tions with constant coefficients. Math. Ann. 176 (1968), 77-86. · Zbl 0161.29802 · doi:10.1007/BF02052957 · eudml:161681
[6] Malgrange, B., Existence et approximation des solutions des equations aux derivees partielles et des equation de convolution, Ann. Inst. Fourier, Grenoble 6 (1955-1956), 271-355. · Zbl 0071.09002 · doi:10.5802/aif.65 · numdam:AIF_1956__6__271_0 · eudml:73728
[7] Narashimhan, R., Introduction to the theory of analytic spaces, Lecture Notes 25, Springer- Verlag, 1966. · Zbl 0168.06003 · doi:10.1007/BFb0077071
[8] Siu, Y, T., Analytic sheaf cohomology groups of dimension n of ra-dimensional non- compact complex manifolds, Pacific J. Math. 28 (1969), 407-411. · Zbl 0182.41504 · doi:10.2140/pjm.1969.28.407
[9] s Analytic sheaf cohomology groups of dimension n of ^-dimensional complex spaces, Trans. Amer. Math. Soc. 143 (1969), 77-94. · Zbl 0186.40404 · doi:10.2307/1995234
[10] Vesentini, E., Lectures on Levi Convexity of Complex Manifolds and Cohomology Vanishing Theorems, Tata Inst. Bombay 1967. · Zbl 0206.36603
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.