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.
Qui proviamo l'esistenza di fibrati vettoriali olomorfi non triviali su ogni varietà complessa 0-convessa ma non Stein e su certe classi di varietà complesse olomorficamente convesse.
@article{BUMI_2006_8_9B_2_261_0, author = {Edoardo Ballico}, title = {Holomorphic vector bundles on certain holomorphically convex complex manifolds}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {9-A}, year = {2006}, pages = {261-265}, zbl = {1178.14008}, mrnumber = {2233136}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2006_8_9B_2_261_0} }
Ballico, Edoardo. Holomorphic vector bundles on certain holomorphically convex complex manifolds. Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006) pp. 261-265. http://gdmltest.u-ga.fr/item/BUMI_2006_8_9B_2_261_0/
[1] Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193-259. | Zbl 0106.05501
and ,[2] Sur l'existence des fibrés holomorphes sur une surface non-algebrique, J. Reine Angew. Math. 378 (1987), 1-31. | Zbl 0624.32017
and ,[3] Über formale komplexe Raume, Manuscripta Math.24 (1978), 253-293.
,[4] On the Oka-Grauert principle for 1-convex manifolds, Math. Ann.310 (1998), 561-569. | Zbl 0902.32011
,[5] Extendability of differential forms on non-isolated singularities, Invent. Math.94 (1988), 317-326. | Zbl 0658.14009
,[6] The Oka-Grauert principle without induction over the base dimension, Math. Ann. 311 (1998), 71-93. | Zbl 0955.32019
and ,[7] Faisceaux sur les variétés analytique-reélles, Bull. Soc. Math. France85 (1957), 231-237.
,[8] | Zbl 0708.17005
, Notes on Lie Algebras, Universitext, Springer, 1990.[9] Analytic sheaf cohomology groups of dimension n of n-dimensional complex spaces, Trans. Amer. Math. Soc.143 (1969), 77-94. | Zbl 0186.40404
,[10] Every compact complex manifold admits a holomorphic vector bundle, Revue Roum. Math. Pures et Appl.38 (1993), 743-744. | Zbl 0813.32025
,[11] Complex analytic geometry of complex parallelizable manifolds, Mémoires Soc. Math. France72-73, 1998. | Zbl 0918.32015
,