### Impacto

Arrondo Esteban, Enrique and Malaspina, Francesco
(2010)
*Cohomological characterization of vector bundles on Grassmannians of lines.*
Journal of Algebra, 323
(4).
pp. 1098-1106.
ISSN 0021-8693

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Official URL: http://www.sciencedirect.com/science/article/pii/S0021869309006061

## Abstract

We introduce a notion of regularity for coherent sheaves on Grassmannians of lines. We use this notion to prove some extension of Evans-Griffith criterion to characterize direct sums of line bundles. We also give. in the line of previous results by Costa and Miro-Roig, a cohomological characterization of exterior and symmetric powers of the universal bundles of the Grassmannian.

Item Type: | Article |
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Uncontrolled Keywords: | Castelnuovo-Mumford regularity; Criterion; Quadrics; Spaces |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 14754 |

References: | [1] E. Arrondo, B. Graña, Vector bundles on G(1, 4) without intermediate cohomology, J. Algebra 214 (1999) 128–142. [2] E. Ballico, F. Malaspina, Qregularity and an extension of the Evans–Griffiths criterion to vector bundles on quadrics, J. Pure Appl. Algebra 213 (2009) 194–202. [3] J.V. Chipalkatti, A generalization of Castelnuovo regularity to Grassmann varieties, Manuscripta Math. 102 (4) (2000) 447– 464. [4] L. Costa, R.M. Miró-Roig, Cohomological characterization of vector bundles on multiprojective spaces, J. Algebra 294 (1) (2005) 73–96, with a corrigendum in: J. Algebra 319 (3) (2008) 1336–1338. [5] L. Costa, R.M. Miró-Roig, m-blocks collections and Castelnuovo–Mumford regularity in multiprojective spaces, Nagoya Math. J. 186 (2007) 119–155. [6] E.G. Evans, P. Griffith, The syzygy problem, Ann. of Math. 114 (2) (1981) 323–333. [7] J.W. Hoffman, H.H. Wang, Castelnuovo–Mumford regularity in biprojective spaces, Adv. Geom. 4 (4) (2004) 513–536. [8] H. Knörrer, Cohen–Macaulay modules on hypersurface singularities I, Invent. Math. 88 (1987) 153–164. [9] F. Malaspina, Few splitting criteria for vector bundles, Ric. Mat. 57 (2008) 55–64. [10] D. Mumford, Lectures on Curves on an Algebraic Surface, Princeton University Press, Princeton, NJ, 1966. [11] G. Ottaviani, Some extension of Horrocks criterion to vector bundles on Grassmannians and quadrics, Ann. Mat. Pura Appl. (IV) 155 (1989) 317–341. |

Deposited On: | 17 Apr 2012 11:32 |

Last Modified: | 06 Feb 2014 10:08 |

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