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Comptes Rendus Mathématique
Volume 351, n° 13-14
pages 557-560 (juillet 2013)
Doi : 10.1016/j.crma.2013.07.018
Received : 26 April 2013 ;  accepted : 23 July 2013
Cubic symmetroids and vector bundles on a quadric surface
Cubiques symétroïdes et fibrés vectoriels sur une surface quadrique

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


We investigate the jumping conics of stable vector bundles   of rank 2 on a smooth quadric surface Q with the Chern classes   and   with respect to the ample line bundle  . As a consequence, we prove that the set of jumping conics   uniquely determines   and that the moduli space of such bundles is rational.

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Nous étudions les coniques de saut des fibrés vectoriels stables   de rang 2 sur une surface quadratique lisse Q de classes de Chern   et   relativement au fibré en droites ample  . Nous en déduisons que lʼensemble des coniques de saut   détermine   de maniére unique et que lʼespace de modules de ce type de fibrés est rationnel.

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1  The author is supported by the Basic Science Research Program 2010-0009195 through NRF funded by MEST.

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