Vector bundles on manifolds without divisors and a theorem on deformations

Georges Elencwajg; O. Forster

Annales de l'institut Fourier (1982)

  • Volume: 32, Issue: 4, page 25-51
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Elencwajg, Georges, and Forster, O.. "Vector bundles on manifolds without divisors and a theorem on deformations." Annales de l'institut Fourier 32.4 (1982): 25-51. <http://eudml.org/doc/74563>.

@article{Elencwajg1982,
abstract = {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.},
author = {Elencwajg, Georges, Forster, O.},
journal = {Annales de l'institut Fourier},
keywords = {manifolds without divisors; holomorphic vector bundles; deformation of bundles; non-algebraic compact manifold},
language = {eng},
number = {4},
pages = {25-51},
publisher = {Association des Annales de l'Institut Fourier},
title = {Vector bundles on manifolds without divisors and a theorem on deformations},
url = {http://eudml.org/doc/74563},
volume = {32},
year = {1982},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 32
IS - 4
SP - 25
EP - 51
AB - 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.
LA - eng
KW - manifolds without divisors; holomorphic vector bundles; deformation of bundles; non-algebraic compact manifold
UR - http://eudml.org/doc/74563
ER -

References

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  1. [1] M. ATIYAH, Vector bundles on elliptic curves, Proc. London Math. Soc., 7 (1957), 414-452. Zbl0084.17305MR24 #A1274
  2. [2] M. ATIYAH, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc., 85 (1957), 181-207. Zbl0078.16002MR19,172c
  3. [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. Zbl0326.14009MR58 #22085
  4. [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. Zbl0146.31103MR34 #2940
  5. [5] Y. MATSUSHIMA, Fibrés holomorphes sur un tore complexe, Nagoya Math. J., 14 (1959), 1-24. Zbl0095.36702MR21 #1403
  6. [6] D. MUMFORD, Abelian varieties, Oxford Univ., Press 1970. Zbl0223.14022MR44 #219
  7. [7] T. ODA, Vector bundles on abelian surfaces, Invent. Math., 13 (1974), 247-260. Zbl0216.05903MR47 #6701
  8. [8] J.-P. SERRE, Sur les modules projectifs, Séminaire Dubreil-Pisot 1960/1961, Exp. 2. Zbl0132.41301
  9. [9] A. WEIL, Variétés Kählériennes. Paris, 1971. 

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