On Buchsbaum bundles on quadric hypersurfaces |
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Authors: | Edoardo Ballico Francesco Malaspina Paolo Valabrega Mario Valenzano |
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Institution: | 1.Dipartimento di Matematica,Università di Trento,Povo,Italy;2.Dipartimento di Matematica,Politecnico di Torino,Torino,Italy;3.Dipartimento di Matematica,Università di Torino,Torino,Italy |
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Abstract: | Let E be an indecomposable rank two vector bundle on the projective space ℙ
n
, n ≥ 3, over an algebraically closed field of characteristic zero. It is well known that E is arithmetically Buchsbaum if and only if n = 3 and E is a null-correlation bundle. In the present paper we establish an analogous result for rank two indecomposable arithmetically
Buchsbaum vector bundles on the smooth quadric hypersurface Q
n
⊂ ℙ
n+1, n ≥ 3. We give in fact a full classification and prove that n must be at most 5. As to k-Buchsbaum rank two vector bundles on Q
3, k ≥ 2, we prove two boundedness results. |
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Keywords: | |
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