Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



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

Authors: N. Mohan Kumar, Chris Peterson and A. Prabhakar Rao
Journal: J. Algebraic Geom. 11 (2002), 203-217
Published electronically: November 20, 2001
MathSciNet review: 1874112
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Abstract | References | Additional Information

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 $p$, 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 $S_5$ in $\mathbf{P}^6$.

References [Enhancements On Off] (What's this?)

  • 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 $n-1$ 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.

Additional Information

N. Mohan Kumar
Affiliation: Department of Mathematics, Washington University, Saint Louis, Missouri 63130

Chris Peterson
Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523

A. Prabhakar Rao
Affiliation: Department of Mathematics, University of Missouri - Saint Louis, Saint Louis, Missouri 63121

Received by editor(s): May 11, 2000
Published electronically: November 20, 2001

American Mathematical Society