Vector bundles on manifolds without divisors and a theorem on deformations
Annales de l'Institut Fourier, Volume 32 (1982) no. 4, pp. 25-51.

We study holomorphic vector bundles on non-algebraic compact manifolds, especially on tori. We exhibit phenomena which cannot occur in the algebraic case, e.g. the existence of 2-bundles that cannot be obtained as extensions of a sheaf of ideals by a line bundle. We prove some general theorems in deformations theory of bundles, which is our main tool.

Nous étudions des fibrés vectoriels holomorphes sur des variétés compactes non algébriques, notamment les tores. Nous mettons en évidence des phénomènes impossibles dans le cas algébrique; ainsi, il existe des fibrés de rang 2 qu’on ne peut pas obtenir comme extension d’un faisceau d’idéaux par un fibré en droites. Nous prouvons quelques résultats généraux sur les déformations de fibrés, lesquelles sont notre principal outil.

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Elencwajg, Georges; Forster, O. Vector bundles on manifolds without divisors and a theorem on deformations. Annales de l'Institut Fourier, Volume 32 (1982) no. 4, pp. 25-51. doi : 10.5802/aif.893. https://aif.centre-mersenne.org/articles/10.5802/aif.893/

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