Fiberwise stable bundles on elliptic threefolds with relative Picard number one

Andrei Căldăraru

doi:10.1016/S1631-073X(02)02290-2

Fiberwise stable bundles on elliptic threefolds with relative Picard number one
[Fibrés vectoriels relativement stables sur variétés elliptiques de dimension trois dont le nombre relatif de Picard est un]

Andrei Căldăraru ¹

¹ Mathematics Department, University of Massachusetts, Amherst, MA 01003, USA

Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 469-472.

Résumé
Abstract

Nous prouvons que les fibrés vectoriels relativement stables sont préservés par des transformées de Fourier–Mukai entre variétés elliptiques de dimension trois dont le nombre relatif de Picard est un. En utilisant ces fibrés nous définissons des nouveaux invariants de variétés elliptiques, et nous étudions la relation entre les invariants d'une variété et ceux d'un éspace relatif de modules des fibrés stables sur elle. Ces résultats nous permettent de calculer la forme d'intersection sur un certain nouvel exemple de variété de Calabi–Yau de dimension trois.

We show that fiberwise stable vector bundles are preserved by relative Fourier–Mukai transforms between elliptic threefolds with relative Picard number one. Using these bundles we define new invariants of elliptic fibrations, and we relate the invariants of a space with those of a relative moduli space of stable sheaves on it. As a byproduct, we calculate the intersection form of a certain new example of an elliptic Calabi–Yau threefold.

Reçu le : 2001-11-29
Accepté le : 2002-01-07
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02290-2

Affiliations des auteurs :

Andrei Căldăraru ¹

¹ Mathematics Department, University of Massachusetts, Amherst, MA 01003, USA

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     title = {Fiberwise stable bundles on elliptic threefolds with relative {Picard} number one},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {469--472},
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Andrei Căldăraru. Fiberwise stable bundles on elliptic threefolds with relative Picard number one. Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 469-472. doi : 10.1016/S1631-073X(02)02290-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02290-2/

Bibliographie
Cité par

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