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 ; Halanay, Andrei D. ; Trautmann, Günther

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 3137479 | Zbl 1299.14037

DOI : https://doi.org/10.5802/aif.2783
Classification : 14J60, 32L05, 14D22, 14F05, 32J17, 32Q25
Mots clés : Fibrés elliptiques principaux non-kählÃ©riens, varietés de dimension 3 de type Calabi-Yau, fibrés vectoriels holomorphes, espaces de modules

@article{AIF_2013__63_3_1033_0,
     author = {Br\^\i nz\u anescu, Vasile and Halanay, Andrei D. and Trautmann, G\"unther},
     title = {Vector bundles on non-Kaehler elliptic principal bundles},
     journal = {Annales de l'Institut Fourier},
     pages = {1033--1054},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {63},
     number = {3},
     year = {2013},
     doi = {10.5802/aif.2783},
     mrnumber = {3137479},
     zbl = {1299.14037},
     language = {en},
     url = {www.numdam.org/item/AIF_2013__63_3_1033_0/}
}

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/item/AIF_2013__63_3_1033_0/

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