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
DOI:
https://doi.org/10.1090/S1056-3911-01-00309-5
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 $\mathbf {P}^6$.
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Ancona V. Ancona and G. Ottaviani, The Horrocks bundles of rank three on ${P}^ 5$, J. Reine Angew. Math. 460 (1995), 69–92.
EG G. Evans and P. Griffith, Syzygies, London Mathematical Society Lecture Note Series Vol. 106, Cambridge University Press, 1985.
HM G. Horrocks and D. Mumford, A rank 2 vector bundle on $\mathbf {P}^4$ with 15,000 symmetries, Topology 12 (1973), 63–81.
Horrocks 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.
Horrocks2 G. Horrocks, Examples of rank three vector bundles on five-dimensional projective space, Journal of the London Mathematical Society 18 (1978), 15–27.
Mohan2 N. Mohan Kumar, Construction of rank two vector bundles on $\mathbf {P}^4$ in positive characteristic, Inventiones Mathematicae 130 (1997), 277–286.
Tango1 H. Tango, An example of indecomposable vector bundle of rank $n-1$ on $\mathbf {P}^4$, Journal of Mathematics of Kyoto University 16 no. 1 (1976), 137–141.
Tango2 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.
Vett U. Vetter, Zu einem Satz von G. Trautmann über den Rang gewisser kohärenter analytischer Moduln, Archiv der Mathematik (Basel) 24 (1973), 158–161.
Sas 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.
Ancona V. Ancona and G. Ottaviani, The Horrocks bundles of rank three on ${P}^ 5$, J. Reine Angew. Math. 460 (1995), 69–92.
EG G. Evans and P. Griffith, Syzygies, London Mathematical Society Lecture Note Series Vol. 106, Cambridge University Press, 1985.
HM G. Horrocks and D. Mumford, A rank 2 vector bundle on $\mathbf {P}^4$ with 15,000 symmetries, Topology 12 (1973), 63–81.
Horrocks 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.
Horrocks2 G. Horrocks, Examples of rank three vector bundles on five-dimensional projective space, Journal of the London Mathematical Society 18 (1978), 15–27.
Mohan2 N. Mohan Kumar, Construction of rank two vector bundles on $\mathbf {P}^4$ in positive characteristic, Inventiones Mathematicae 130 (1997), 277–286.
Tango1 H. Tango, An example of indecomposable vector bundle of rank $n-1$ on $\mathbf {P}^4$, Journal of Mathematics of Kyoto University 16 no. 1 (1976), 137–141.
Tango2 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.
Vett 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
Email:
kumar@math.wustl.edu
Chris Peterson
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
MR Author ID:
359254
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
Received by editor(s):
May 11, 2000
Published electronically:
November 20, 2001
