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

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.

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.

@article{AIF_1982__32_4_25_0,
     author = {Elencwajg, Georges and Forster, O.},
     title = {Vector bundles on manifolds without divisors and a theorem on deformations},
     journal = {Annales de l'Institut Fourier},
     pages = {25--51},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {32},
     number = {4},
     year = {1982},
     doi = {10.5802/aif.893},
     mrnumber = {84f:32035},
     zbl = {0488.32012},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.893/}
}
TY  - JOUR
AU  - Elencwajg, Georges
AU  - Forster, O.
TI  - Vector bundles on manifolds without divisors and a theorem on deformations
JO  - Annales de l'Institut Fourier
PY  - 1982
SP  - 25
EP  - 51
VL  - 32
IS  - 4
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/articles/10.5802/aif.893/
DO  - 10.5802/aif.893
LA  - en
ID  - AIF_1982__32_4_25_0
ER  - 
%0 Journal Article
%A Elencwajg, Georges
%A Forster, O.
%T Vector bundles on manifolds without divisors and a theorem on deformations
%J Annales de l'Institut Fourier
%D 1982
%P 25-51
%V 32
%N 4
%I Institut Fourier
%C Grenoble
%U http://archive.numdam.org/articles/10.5802/aif.893/
%R 10.5802/aif.893
%G en
%F AIF_1982__32_4_25_0
Elencwajg, Georges; Forster, O. Vector bundles on manifolds without divisors and a theorem on deformations. Annales de l'Institut Fourier, Tome 32 (1982) no. 4, pp. 25-51. doi : 10.5802/aif.893. http://archive.numdam.org/articles/10.5802/aif.893/

[1] M. Atiyah, Vector bundles on elliptic curves, Proc. London Math. Soc., 7 (1957), 414-452. | MR | Zbl

[2] M. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc., 85 (1957), 181-207. | MR | Zbl

[3] E. Bombieri and D. Husemoller, Classification and embeddings of surfaces, In : Algebraic Geometry, Arcata 1974, AMS Proc. Symp. Pure Math., 29 (1975), 329-420. | MR | Zbl

[4] A. Douady, Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Ann. Inst. Fourier, 16 (1966), 1-95. | Numdam | MR | Zbl

[5] Y. Matsushima, Fibrés holomorphes sur un tore complexe, Nagoya Math. J., 14 (1959), 1-24. | MR | Zbl

[6] D. Mumford, Abelian varieties, Oxford Univ., Press 1970. | MR | Zbl

[7] T. Oda, Vector bundles on abelian surfaces, Invent. Math., 13 (1974), 247-260. | MR | Zbl

[8] J.-P. Serre, Sur les modules projectifs, Séminaire Dubreil-Pisot 1960/1961, Exp. 2. | Numdam | Zbl

[9] A. Weil, Variétés Kählériennes. Paris, 1971.

Cité par Sources :