Arrondo Esteban, Enrique and Graña Otero, Beatriz
(1999)
*Vector bundles on G(1,4) without intermediate cohomology.*
Journal of Algebra, 214
(1).
pp. 128-142.
ISSN 0021-8693

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Official URL: http://www.sciencedirect.com/science/article/pii/S0021869398977006

## Abstract

It is a famous result due to G. Horrocks [Proc. Lond. Math. Soc. (3) 14, 689-713 (1964;

Zbl 0126.16801)] that line bundles on a projective space are the only indecomposable

vector bundles without intermediate cohomology. This fact generalizes to quadric and

grassmannians if we add cohomological conditions.

In this paper the case of G(1, 4) is studied completely, and a characterization-classification

of vector bundles on it without intermediate cohomology is obtained.

Item Type: | Article |
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Uncontrolled Keywords: | Cohen_Macaulay modules; hypersurface singularities |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 14838 |

References: | wACx E. Arrondo and L. Costa, Vector bundles on Fano 3-folds without intermediate cohomology, preprint, 1998. wASx E. Arrondo and I. Sols, On congruences of lines in the projective space, M´em. Soc. Math. France 50 �1992.. wBGSx R. O. Buchweitz, G. M. Greuel, and F. O. Schreyer, Cohen]Macaulay modules on hypersurface singularities, II, In¨ent. Math. 88 �1987., 165]182. wHx G. Horrocks, Vector bundles on the punctured spectrum of a ring, Proc. London Math. Soc. �3. 14 �1964., 689]713. wKSx S. Katz and S. A. Strømme, Schubert, a Maple package for intersection theory, available at http:rrwww.math.okstaste.edur;;katzrschubert.html or by anonymous ftp from ftp.math.okstate.edu or linus.mi.uib.no, cd pubrschubert. wKx H. Kn¨orrer, Cohen]Macaulay modules on hypersurface singularities, I, In¨ent. Math. 88 �1987., 153]164. wMx C. Madonna, A splitting criterion for rank 2 vector bundles on hypersurfaces in P4, Rend. Sem. Torino, in press. wO1x G. Ottaviani, Crit`eres de scindage pour les fibr´es vectoriels sur les grassmannianes et les quadriques, C.R. Acad. Sci. Paris S´er. I 305 �1987., 257]260. wO2x G. Ottaviani, Some extensions of Horrocks criterion to vector bundles on Grassman- nians and quadrics, Ann. Mat. Pura Appl. �4. 155 �1989., 317]341. |

Deposited On: | 18 Apr 2012 10:02 |

Last Modified: | 06 Feb 2014 10:10 |

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