Rungescher Satz and a condition for Steiness for the limit of an increasing sequence of Stein spaces

Alessandro Silva

Annales de l'institut Fourier (1978)

  • Volume: 28, Issue: 2, page 187-200
  • ISSN: 0373-0956

Abstract

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A necessary and sufficient condition, which is a weak converse of a classical theorem of Behnke-Stein, in order that a limit of Stein spaces be again a Stein space is proved.

How to cite

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Silva, Alessandro. "Rungescher Satz and a condition for Steiness for the limit of an increasing sequence of Stein spaces." Annales de l'institut Fourier 28.2 (1978): 187-200. <http://eudml.org/doc/74355>.

@article{Silva1978,
abstract = {A necessary and sufficient condition, which is a weak converse of a classical theorem of Behnke-Stein, in order that a limit of Stein spaces be again a Stein space is proved.},
author = {Silva, Alessandro},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {187-200},
publisher = {Association des Annales de l'Institut Fourier},
title = {Rungescher Satz and a condition for Steiness for the limit of an increasing sequence of Stein spaces},
url = {http://eudml.org/doc/74355},
volume = {28},
year = {1978},
}

TY - JOUR
AU - Silva, Alessandro
TI - Rungescher Satz and a condition for Steiness for the limit of an increasing sequence of Stein spaces
JO - Annales de l'institut Fourier
PY - 1978
PB - Association des Annales de l'Institut Fourier
VL - 28
IS - 2
SP - 187
EP - 200
AB - A necessary and sufficient condition, which is a weak converse of a classical theorem of Behnke-Stein, in order that a limit of Stein spaces be again a Stein space is proved.
LA - eng
UR - http://eudml.org/doc/74355
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), 193-260. Zbl0106.05501MR27 #343
  2. [2] A. ANDREOTTI et E. VESENTINI, Les Théorèmes fondamentaux de la théorie des espaces holomorphiquement complets, in Sem. Ehresmann, Paris, (1962). 
  3. [3] H. BEHNKE und K. STEIN, Konvergente Folgen von Regularitatsbereichen und die meromorphe Konvexitat, Math. Annalen, 116 (1939), 204-216. Zbl0020.37803JFM64.0322.03
  4. [4] A. CASSA, Coomologia separata sulle varieta analitiche complesse, Annali SNS Pisa, 25 (1971), 291-323. 
  5. [5] J. E. FORNAESS, An increasing sequence of Stein manifolds whose limit is not Stein, Math. Annalen, 223 (1976), 275-277. Zbl0334.32017MR54 #5498
  6. [6] A. GROTHENDIECK, Sur quelques points d'algèbre homologique, Tôhoku Math. Journal, II, 9 (1957), 119-183. Zbl0118.26104MR21 #1328
  7. [7] A. HIRSCHOWITZ, Pseudoconvexité au-dessus d'espaces plus ou moins homogènes, Inventiones Math., 26 (1974), 303-322. Zbl0275.32009MR50 #10323
  8. [8] Y. T. SIU, Non countable dimension of cohomology groups of analytic sheaves and domains of holomorphy, Math. Zeit., 102 (1967), 17-29. Zbl0167.06802MR36 #5394
  9. [9] F. TREVES, Locally convex spaces and linear partial differential equations, Springer, Berlin (1967). Zbl0152.32104MR36 #6986
  10. [10] V. VILLANI, Un teorema di passaggio al limite per la coomologia degli spazi complessi, Rend. Sc. fis. mat. e nat. Accad. Lincei, 43 (1967), 168-170. Zbl0157.40501MR37 #6487
  11. [11] J. WERMER, An example concerning polynomial convexity, Math. Annalen, 139 (1959), 147-150. Zbl0094.28302MR22 #12238
  12. [12] A. MARKOE, Runge families and inductive limits of Stein spaces, Ann. Inst. Fourier, 27 (1977), 117-128. Zbl0323.32014MR58 #28665
  13. [13] J.-P. RAMIS, G. RUGET et J. L. VERDIER, Dualité Relative en Géométrie Analytique Complexe, Inv. Math., 13 (1971), 261-283. Zbl0218.14010MR46 #7553
  14. [14] A. OGUS, Local cohomological dimension, Ann. of Math., 98 (1973), 327-365. Zbl0308.14003MR58 #22059

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