# On Buchsbaum bundles on quadric hypersurfaces

Edoardo Ballico; Francesco Malaspina; Paolo Valabrega; Mario Valenzano

Open Mathematics (2012)

- Volume: 10, Issue: 4, page 1361-1379
- ISSN: 2391-5455

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topEdoardo Ballico, et al. "On Buchsbaum bundles on quadric hypersurfaces." Open Mathematics 10.4 (2012): 1361-1379. <http://eudml.org/doc/269458>.

@article{EdoardoBallico2012,

abstract = {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.},

author = {Edoardo Ballico, Francesco Malaspina, Paolo Valabrega, Mario Valenzano},

journal = {Open Mathematics},

keywords = {Arithmetically Buchsbaum rank two vector bundles; Smooth quadric hypersurfaces; arithmetically Buchsbaum rank two vector bundles; smooth quadric hypersurfaces},

language = {eng},

number = {4},

pages = {1361-1379},

title = {On Buchsbaum bundles on quadric hypersurfaces},

url = {http://eudml.org/doc/269458},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Edoardo Ballico

AU - Francesco Malaspina

AU - Paolo Valabrega

AU - Mario Valenzano

TI - On Buchsbaum bundles on quadric hypersurfaces

JO - Open Mathematics

PY - 2012

VL - 10

IS - 4

SP - 1361

EP - 1379

AB - 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.

LA - eng

KW - Arithmetically Buchsbaum rank two vector bundles; Smooth quadric hypersurfaces; arithmetically Buchsbaum rank two vector bundles; smooth quadric hypersurfaces

UR - http://eudml.org/doc/269458

ER -

## References

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