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arXiv · 1112.3572

A refined stable restriction theorem for vector bundles on quadric threefolds

Iustin Coanda·Daniele Faenzi
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Abstract

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)].

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Iustin Coanda, Daniele Faenzi. 2012-11-28. A refined stable restriction theorem for vector bundles on quadric threefolds. https://doi.org/10.1007/s10231-012-0304-8

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