Holomorphic vector bundles on non-algebraic surfacesFibrés vectoriels holomorphes sur les surfaces non algébriques |
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| Authors: | Andrei Teleman Matei Toma |
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| Institution: | 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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| Abstract: | 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. To cite this article: A. Teleman, M. Toma, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 383–388. |
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