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Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology

100%

Ballico E., Malaspina F.

Open Mathematics

2008

tom 6

nr 1

143-148

Here we study vector bundles E on the Hirzebruch surface F e such that their twists by a spanned, but not ample, line bundle M = $$ \mathcal{O} $$ Fe(h + ef) have natural cohomology, i.e. h 0(F e, E(tM)) > 0 implies h 1(F e, E(tM)) = 0.

On Buchsbaum bundles on quadric hypersurfaces

81%

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

2 Open Mathematics

2 Ballico E.

2 Malaspina F.

1 Valabrega P.

1 Valenzano M.

1 2012

1 2008

Wyniki wyszukiwania

Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology

On Buchsbaum bundles on quadric hypersurfaces