Vector bundles on non-Kaehler elliptic principal bundles

Brînzănescu, Vasile; Halanay, Andrei D.; Trautmann, Günther

doi:10.5802/aif.2783

Vector bundles on non-Kaehler elliptic principal bundles
[Fibrés vectoriels sur des fibrés principaux elliptiques non-kähleriens]

Brînzănescu, Vasile ¹ ; Halanay, Andrei D.² ; Trautmann, Günther ³

¹ “Simion Stoilow” Institute of Mathematics of the Romanian Academy P.O.Box 1-764, 014700 Bucharest (Romania)
² University of Bucharest Faculty of Mathematics and Computer Science Str. Academiei 14 010014 Bucharest (Romania)
³ Universität Kaiserslautern Fachbereich Mathematik Erwin-Schrödinger-Straße D-67663 Kaiserslautern (Allemagne)

Annales de l'Institut Fourier, Tome 63 (2013) no. 3, pp. 1033-1054.

Résumé
Abstract

Nous étudions les fibrés vectoriels relativement semi-stables sur des varietés non-kählériennes qui sont des fibrés principaux elliptiques. Les principaux outils techniques utilisés sont la transformée de Fourier-Mukai tordue et une construction de revêtement spectral. Pour un exemple important de ces fibrés principaux, nous calculons les invariants numériques des fibrés elliptiques sur une surface de Kodaira primaire.

We study relatively semi-stable vector bundles and their moduli on non-Kähler principal elliptic bundles over compact complex manifolds of arbitrary dimension. The main technical tools used are the twisted Fourier-Mukai transform and a spectral cover construction. For the important example of such principal bundles, the numerical invariants of a 3-dimensional non-Kähler elliptic principal bundle over a primary Kodaira surface are computed.

MR Zbl

DOI : 10.5802/aif.2783

Classification : 14J60, 32L05, 14D22, 14F05, 32J17, 32Q25
Keywords: non-Kähler principal elliptic bundles, Calabi-Yau type threefolds, holomorphic vector bundles, moduli spaces
Mot clés : Fibrés elliptiques principaux non-kählÃ©riens, varietés de dimension 3 de type Calabi-Yau, fibrés vectoriels holomorphes, espaces de modules

Affiliations des auteurs :

Brînzănescu, Vasile ¹ ; Halanay, Andrei D. ² ; Trautmann, Günther ³

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     title = {Vector bundles on {non-Kaehler} elliptic principal bundles},
     journal = {Annales de l'Institut Fourier},
     pages = {1033--1054},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Brînzănescu, Vasile; Halanay, Andrei D.; Trautmann, Günther. Vector bundles on non-Kaehler elliptic principal bundles. Annales de l'Institut Fourier, Tome 63 (2013) no. 3, pp. 1033-1054. doi : 10.5802/aif.2783. http://www.numdam.org/articles/10.5802/aif.2783/

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