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: 0392-4033

Abstract

top
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

top

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

top
  1. ANDREOTTI, A. and GRAUERT, H., Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France90 (1962), 193-259. Zbl0106.05501
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.