Fiberwise stable bundles on elliptic threefolds with relative Picard number one
Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 469-472.

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.

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.

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DOI: 10.1016/S1631-073X(02)02290-2
Căldăraru, Andrei 1

1 Mathematics Department, University of Massachusetts, Amherst, MA 01003, USA
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Căldăraru, Andrei. 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. http://www.numdam.org/articles/10.1016/S1631-073X(02)02290-2/

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