Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces

Brînzănescu, Vasile; Moraru, Ruxandra

doi:10.5802/aif.2135

Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces
[Fibrés holomorphes de rang 2 sur des surfaces elliptiques non-kähleriennes]

Brînzănescu, Vasile ¹ ; Moraru, Ruxandra

¹ Institute of Mathematics Simion Stoilow, Romanian Academy, PO Box 1-764, RO-70700, Bucharest (Roumanie), University of Toronto, department of mathematics, 100 St George Street, Toronto, Ontario M5S 3G3 (Canada)

Annales de l'Institut Fourier, Tome 55 (2005) no. 5, pp. 1659-1683.

Résumé
Abstract

Dans cet article, nous étudions l'existence de structures holomorphes pour les fibrés de rang 2 sur des surfaces elliptiques non-kähleriennes ; entre autres, nous donnons des conditions nécessaires et suffisantes pour l'existence de fibrés holomorphes de rang 2 sur des surfaces elliptiques non-kähleriennes.

In this paper, we consider the problem of determining which topological complex rank-2 vector bundles on non-Kähler elliptic surfaces admit holomorphic structures; in particular, we give necessary and sufficient conditions for the existence of holomorphic rank-2 vector bundles on non-{Kä}hler elliptic surfaces.

MR Zbl

DOI : 10.5802/aif.2135

Classification : 14J60, 14D22, 14F05, 14J27, 32J15
Keywords: Non-Kähler surfaces, ellipic surfaces, holomorphic vector bundles
Mot clés : surfaces non-kähleriennes, surfaces elliptiques, fibrés vectoriels holomorphes

Affiliations des auteurs :

Brînzănescu, Vasile ¹ ; Moraru, Ruxandra

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     author = {Br{\^\i}nz\u{a}nescu, Vasile and Moraru, Ruxandra},
     title = {Holomorphic rank-2 vector bundles on {non-K\"ahler} elliptic surfaces},
     journal = {Annales de l'Institut Fourier},
     pages = {1659--1683},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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     mrnumber = {2172276},
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Brînzănescu, Vasile; Moraru, Ruxandra. Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces. Annales de l'Institut Fourier, Tome 55 (2005) no. 5, pp. 1659-1683. doi : 10.5802/aif.2135. http://www.numdam.org/articles/10.5802/aif.2135/

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