Complutense University Library

Vector bundles on G(1,4) without intermediate cohomology

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

[img] PDF
Restricted to Repository staff only until 2020.

103kB

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

View download statistics for this eprint

==>>> Export to other formats

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
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

Repository Staff Only: item control page