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On Buchsbaum bundles on quadric hypersurfaces. (English) Zbl 1282.14031
If \(E\) is a vector bundle on a polarized projective variety \((X,L)\), it is called arithmetically Cohen-Macaulay if all its intermediate cohomologies vanish for all twists of \(L\). It is called arithmetically Buchsbaum, if the intermediate cohomologies have trivial vector space structure over the ring \(\bigoplus H^0(L^n)\) and it is properly arithmetically Buchsbaum, if it is in addition not arithmetically Cohen-Macaulay. It is well known that if the variety is \((\mathbb{P}^n,\mathcal{O}_{\mathbb{P}^n}(1))\), and \(E\) is indecomposable rank two vector bundle in characteristic zero (so it is properly arithmetically Buchsbaum, by a theorem of Horrocks), then \(n=3\) and \(E\) is the null-correlation bundle. In the paper under review, the authors completely classify properly arithmetically Buchsbaum bundles of rank 2 on smooth quadrics \(Q_n\) in \(\mathbb{P}^{n+1}\)

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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