Algebraic Geometry
Cubic symmetroids and vector bundles on a quadric surface
Comptes Rendus. Mathématique, Volume 351 (2013) no. 13-14, pp. 557-560.

We investigate the jumping conics of stable vector bundles E of rank 2 on a smooth quadric surface Q with the Chern classes c1=OQ(1,1) and c2=4 with respect to the ample line bundle OQ(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 c1=OQ(1,1) et c2=4 relativement au fibré en droites ample OQ(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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.07.018
Huh, Sukmoon 1

1 Department of Mathematics, Sungkyunkwan University, 300 Cheoncheon-dong, Suwon 440-746, Republic of Korea
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Huh, Sukmoon. 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. http://www.numdam.org/articles/10.1016/j.crma.2013.07.018/

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