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On Buchsbaum bundles on quadric hypersurfaces

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Ballico E., Malaspina F., Valabrega P., Valenzano M.

Open Mathematics

2012

tom 10

nr 4

1361-1379

Let E be an indecomposable rank two vector bundle on the projective space ℙn, 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 ⊂ ℙn+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.

Ograniczanie wyników

1 Open Mathematics

1 Ballico E.

1 Malaspina F.

1 Valabrega P.

1 Valenzano M.

1 2012

Wyniki wyszukiwania

On Buchsbaum bundles on quadric hypersurfaces