Cubic symmetroids and vector bundles on a quadric surface

Sukmoon Huh

doi:10.1016/j.crma.2013.07.018

Algebraic Geometry

Cubic symmetroids and vector bundles on a quadric surface

Presented by: Claire Voisin

Sukmoon Huh ¹

¹ Department of Mathematics, Sungkyunkwan University, 300 Cheoncheon-dong, Suwon 440-746, Republic of Korea

Comptes Rendus. Mathématique, Volume 351 (2013) no. 13-14, pp. 557-560.

Abstract (Original language)
Résumé

We investigate the jumping conics of stable vector bundles $E$ of rank 2 on a smooth quadric surface Q with the Chern classes $c_{1} = O_{Q} (- 1, - 1)$ and $c_{2} = 4$ with respect to the ample line bundle $O_{Q} (1, 1)$ . As a consequence, we prove that the set of jumping conics $S (E)$ uniquely determines $E$ and that the moduli space of such bundles is rational.

Nous étudions les coniques de saut des fibrés vectoriels stables $E$ de rang 2 sur une surface quadratique lisse Q de classes de Chern $c_{1} = O_{Q} (- 1, - 1)$ et $c_{2} = 4$ relativement au fibré en droites ample $O_{Q} (1, 1)$ . Nous en déduisons que lʼensemble des coniques de saut $S (E)$ détermine $E$ de maniére unique et que lʼespace de modules de ce type de fibrés est rationnel.

Received: 2013-04-26
Accepted: 2013-07-23
Published online: 2013-07-01

DOI: 10.1016/j.crma.2013.07.018

Author's affiliations:

Sukmoon Huh ¹

¹ Department of Mathematics, Sungkyunkwan University, 300 Cheoncheon-dong, Suwon 440-746, Republic of Korea

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Sukmoon Huh. Cubic symmetroids and vector bundles on a quadric surface. Comptes Rendus. Mathématique, Volume 351 (2013) no. 13-14, pp. 557-560. doi : 10.1016/j.crma.2013.07.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.07.018/

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