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Article Dans Une Revue Annali di Matematica Pura ed Applicata Année : 2014

A refined stable restriction theorem for vector bundles on quadric threefolds

Résumé

Let E be a stable rank 2 vector bundle on a smooth quadric threefold Q in the projective 4-space P. We show that the hyperplanes H in P for which the restriction of E to the hyperplane section of Q by H is not stable form, in general, a closed subset of codimension at least 2 of the dual projective 4-space, and we explicitly describe the bundles E which do not enjoy this property. This refines a restriction theorem of Ein and Sols [Nagoya Math. J. 96, 11-22 (1984)] in the same way the main result of Coanda [J. reine angew. Math. 428, 97-110 (1992)] refines the restriction theorem of Barth [Math. Ann. 226, 125-150 (1977)].

Dates et versions

hal-00664088 , version 1 (28-01-2012)

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Iustin Coanda,, Daniele Faenzi. A refined stable restriction theorem for vector bundles on quadric threefolds. Annali di Matematica Pura ed Applicata, 2014, 193 (3), pp.859-887. ⟨10.1007/s10231-012-0304-8⟩. ⟨hal-00664088⟩
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