[Fibrés vectoriels holomorphes sur les surfaces non algébriques]
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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@article{CRMATH_2002__334_5_383_0,
author = {Teleman, Andrei and Toma, Matei},
title = {Holomorphic vector bundles on non-algebraic surfaces},
journal = {Comptes Rendus. Math\'ematique},
pages = {383--388},
publisher = {Elsevier},
volume = {334},
number = {5},
year = {2002},
doi = {10.1016/S1631-073X(02)02278-1},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02278-1/}
}
TY - JOUR AU - Teleman, Andrei AU - Toma, Matei TI - Holomorphic vector bundles on non-algebraic surfaces JO - Comptes Rendus. Mathématique PY - 2002 SP - 383 EP - 388 VL - 334 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02278-1/ DO - 10.1016/S1631-073X(02)02278-1 LA - en ID - CRMATH_2002__334_5_383_0 ER -
%0 Journal Article %A Teleman, Andrei %A Toma, Matei %T Holomorphic vector bundles on non-algebraic surfaces %J Comptes Rendus. Mathématique %D 2002 %P 383-388 %V 334 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02278-1/ %R 10.1016/S1631-073X(02)02278-1 %G en %F CRMATH_2002__334_5_383_0
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://www.numdam.org/articles/10.1016/S1631-073X(02)02278-1/
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