Holomorphic vector bundles on certain holomorphically convex complex manifolds

Edoardo Ballico

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 2, page 261-265
  • ISSN: 0392-4041

Abstract

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Here we prove the existence of non-trivial holomorphic vector bundles on every 0-convex but not Stein complex manifold and on certain classes of holomorphically convex complex manifolds.

How to cite

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Ballico, Edoardo. "Holomorphic vector bundles on certain holomorphically convex complex manifolds." Bollettino dell'Unione Matematica Italiana 9-B.2 (2006): 261-265. <http://eudml.org/doc/289624>.

@article{Ballico2006,
abstract = {Here we prove the existence of non-trivial holomorphic vector bundles on every 0-convex but not Stein complex manifold and on certain classes of holomorphically convex complex manifolds.},
author = {Ballico, Edoardo},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {261-265},
publisher = {Unione Matematica Italiana},
title = {Holomorphic vector bundles on certain holomorphically convex complex manifolds},
url = {http://eudml.org/doc/289624},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Ballico, Edoardo
TI - Holomorphic vector bundles on certain holomorphically convex complex manifolds
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/6//
PB - Unione Matematica Italiana
VL - 9-B
IS - 2
SP - 261
EP - 265
AB - Here we prove the existence of non-trivial holomorphic vector bundles on every 0-convex but not Stein complex manifold and on certain classes of holomorphically convex complex manifolds.
LA - eng
UR - http://eudml.org/doc/289624
ER -

References

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  2. BANICA, C. and LE POTIER, J., Sur l'existence des fibrés holomorphes sur une surface non-algebrique, J. Reine Angew. Math.378 (1987), 1-31. Zbl0624.32017
  3. BINGENER, J., Über formale komplexe Raume, Manuscripta Math.24 (1978), 253-293. 
  4. COLTOIU, M., On the Oka-Grauert principle for 1-convex manifolds, Math. Ann.310 (1998), 561-569. Zbl0902.32011
  5. FLENNER, H., Extendability of differential forms on non-isolated singularities, Invent. Math.94 (1988), 317-326. Zbl0658.14009
  6. HENKIN, G. and LEITERER, J., The Oka-Grauert principle without induction over the base dimension, Math. Ann.311 (1998), 71-93. Zbl0955.32019
  7. MALGRANGE, B., Faisceaux sur les variétés analytique-reélles, Bull. Soc. Math. France85 (1957), 231-237. 
  8. SAMELSON, H., Notes on Lie Algebras, Universitext, Springer, 1990. Zbl0708.17005
  9. SIU, Y.-T., Analytic sheaf cohomology groups of dimension n of n-dimensional complex spaces, Trans. Amer. Math. Soc.143 (1969), 77-94. Zbl0186.40404
  10. WINKELMANN, J., Every compact complex manifold admits a holomorphic vector bundle, Revue Roum. Math. Pures et Appl.38 (1993), 743-744. Zbl0813.32025
  11. WINKELMANN, J., Complex analytic geometry of complex parallelizable manifolds, Mémoires Soc. Math. France72-73, 1998. Zbl0918.32015

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