A refined stable restriction theorem for vector bundles on quadric threefolds
Algebraic Geometry
2012-11-29 v2
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)].
Cite
@article{arxiv.1112.3572,
title = {A refined stable restriction theorem for vector bundles on quadric threefolds},
author = {Iustin Coanda and Daniele Faenzi},
journal= {arXiv preprint arXiv:1112.3572},
year = {2012}
}
Comments
Ann. Mat. Pura Appl. 2012