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Degenerating families of rank two bundles


Authors: N. Mohan Kumar, Chris Peterson and A. Prabhakar Rao
Journal: Proc. Amer. Math. Soc. 131 (2003), 3681-3688
MSC (2000): Primary 14F05, 13D02, 14J60, 32L05, 13A35
Published electronically: May 8, 2003
MathSciNet review: 1998174
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct families of rank two bundles $\mathcal{E}_t$ on $\mathbf{P}^4$, in characteristic two, where for $t\neq 0$, $\mathcal{E}_t$ is a sum of line bundles, and $\mathcal{E}_0$ is non-split. We construct families of rank two bundles $\mathcal{E}_t$ on $\mathbf{P}^3$, in characteristic $p$, where for $t\neq 0$, $\mathcal{E}_t$ is a sum of line bundles, and $\mathcal{E}_0$ is non-split.


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

  • 1. N. Mohan Kumar, Smooth degeneration of complete intersection curves in positive characteristic, Invent. Math. 104 (1991), no. 2, 313–319. MR 1098612, 10.1007/BF01245078
  • 2. N. Mohan Kumar, Construction of Rank Two Vector Bundles on Projective Spaces. To appear in Proceedings of the Bombay International Colloquium on Algebra, Arithmetic and Geometry, TIFR (2000).
  • 3. Steven L. Kleiman, Geometry on Grassmannians and applications to splitting bundles and smoothing cycles, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 281–297. MR 0265371
  • 4. P. Schwartau, Liaison Addition and Monomial Ideals. Ph.D. Thesis, Brandeis University (1982).
  • 5. Hiroshi Tango, On morphisms from projective space 𝑃ⁿ to the Grassmann variety 𝐺𝑟(𝑛,𝑑), J. Math. Kyoto Univ. 16 (1976), no. 1, 201–207. MR 0401787

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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
Email: peterson@math.colostate.edu

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

DOI: https://doi.org/10.1090/S0002-9939-03-07071-0
Received by editor(s): September 9, 2001
Received by editor(s) in revised form: July 20, 2002
Published electronically: May 8, 2003
Additional Notes: The authors would like to thank the NSF for partial support of this project
Communicated by: Michael Stillman
Article copyright: © Copyright 2003 American Mathematical Society