Journal of Algebraic Geometry

Construction of low rank vector bundles on $\mathbf{P}^{4}$ and $\mathbf{P}^{5}$

Author(s): N. Mohan Kumar; Chris Peterson; A. Prabhakar Rao
Journal: J. Algebraic Geom. 11 (2002), 203-217.
Posted: November 20, 2001
Retrieve article in: PDF DVI PostScript

Abstract: We describe a technique which permits a uniform construction of a number of low rank bundles, both known and new. In characteristic two, we obtain rank two bundles on $\mathbf{P}^{5}$ . In characteristic

, we obtain rank two bundles on $\mathbf{P}^4$ and rank three bundles on $\mathbf{P}^5$ . In arbitrary characteristic, we obtain rank three bundles on $\mathbf{P}^4$ and rank two bundles on the quadric

in $\mathbf{P}^6$ .

1.: H. Abo, W. Decker and N. Sasakura, An elliptic conic bundle in $\mathbf{P}^4$ arising from a stable rank-3 vector bundle, Mathematische Zeitschrift 229 no.4 (1998), 725-741.
2.: V. Ancona and G. Ottaviani, The Horrocks bundles of rank three on ${P}\sp 5$ , J. Reine Angew. Math. 460 (1995), 69-92.
3.: G. Evans and P. Griffith, Syzygies, London Mathematical Society Lecture Note Series Vol. 106, Cambridge University Press, 1985.
4.: G. Horrocks and D. Mumford, A rank 2 vector bundle on $\mathbf{P}^4$ with 15,000 symmetries, Topology 12 (1973), 63-81.
5.: G. Horrocks, Vector bundles on the punctured spectrum of a local ring II, Vector Bundles on Algebraic Varieties (Bombay, 1984), TIFR, Oxford University Press (1987) 207-216.
6.: G. Horrocks, Examples of rank three vector bundles on five-dimensional projective space, Journal of the London Mathematical Society 18 (1978), 15-27.
7.: N. Mohan Kumar, Construction of rank two vector bundles on $\mathbf{P}^4$ in positive characteristic, Inventiones Mathematicae 130 (1997), 277-286.
8.: H. Tango, An example of indecomposable vector bundle of rank on ${\mathbf P}^n$ , Journal of Mathematics of Kyoto University 16 no. 1 (1976), 137-141.
9.: H. Tango, On morphisms from projective space $\mathbf{P}^n$ to the Grassmann variety $\mathbf{Gr}(n, d)$ , Journal of Mathematics of Kyoto University 16 no. 1 (1976), 201-207.
10.: U. Vetter, Zu einem Satz von G. Trautmann über den Rang gewisser kohärenter analytischer Moduln, Archiv der Mathematik (Basel) 24 (1973), 158-161.

N. Mohan Kumar
Affiliation: Department of Mathematics, Washington University, Saint Louis, Missouri 63130
Email: kumar@math.wustl.edu

Chris Peterson
Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
Email: peterson@math.colostate.edu

A. Prabhakar Rao
Affiliation: Department of Mathematics, University of Missouri - Saint Louis, Saint Louis, Missouri 63121
Email: rao@arch.umsl.edu

PII: S 1056-3911(01)00309-5
Received by editor(s): May 11, 2000
Posted: November 20, 2001

Previous issue \| Table of contents \| Next issue Recently posted articles \| Most recent issue \| All issues