Holomorphic vector bundles on non-algebraic surfaces
[Fibrés vectoriels holomorphes sur les surfaces non algébriques]
Comptes Rendus. Mathématique, Tome 334 (2002) no. 5, pp. 383-388.

Le problème de l'existence des structures holomorphes sur les fibrés vectoriels au-dessus des surfaces non algébriques est en général encore ouvert. Nous résolvons ce problème pour les fibrés de rang 2 sur les surfaces K3 et pour les fibrés de rangs arbitraires sur toutes les surfaces connues de la classe VII. Nos méthodes, qui s'appuient sur la théorie de Donaldson et sur la théorie des déformations, peuvent être utilisées pour résoudre le problème de l'existence des fibrés vectoriels holomorphes sur d'autres classes de surfaces non algébriques.

The existence problem for holomorphic structures on vector bundles over non-algebraic surfaces is, in general, still open. We solve this problem in the case of rank 2 vector bundles over K3 surfaces and in the case of vector bundles of arbitrary rank over all known surfaces of class VII. Our methods, which are based on Donaldson theory and deformation theory, can be used to solve the existence problem of holomorphic vector bundles on further classes of non-algebraic surfaces.

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DOI : 10.1016/S1631-073X(02)02278-1
Teleman, Andrei 1, 2 ; Toma, Matei 3, 4

1 CMI, Université de Provence, 39, rue F. Joliot Curie, 13453 Marseille cedex 13, France
2 Faculty of Mathematics, University of Bucharest, Romania
3 Fachbereich Mathematik-Informatik, Universität Osnabrück, 49069 Osnabrück, Germany
4 Mathematical Institute of the Romanian Academy, Romania
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Teleman, Andrei; Toma, Matei. Holomorphic vector bundles on non-algebraic surfaces. Comptes Rendus. Mathématique, Tome 334 (2002) no. 5, pp. 383-388. doi : 10.1016/S1631-073X(02)02278-1. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02278-1/

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