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Monads on projective spaces

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Abstract.

Let ℰ be a vector bundle on P n. There is a strong relationship between ℰ and its intermediate cohomology modules. In the case where ℰ has low rank, we exploit this relationship to provide various splitting criteria for ℰ. In particular, we give a splitting criterion for ℰ in terms of the vanishing of certain intermediate cohomology modules. We also show that the Horrocks-Mumford bundle is the only non-split rank two bundle on P 4 with a Buchsbaum second cohomology module.

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References

  1. Ancona, V., Ottaviani, G.: On moduli of instanton bundles on P 2n+1. Pacific J. Math. 171, 343–351 (1995)

    MathSciNet  MATH  Google Scholar 

  2. Atiyah, M.F., Hitchin, N.J., Drinfeld, V.G., Manin, Ju.: Construction of instantons. Phys. Lett. 65 A, 185–187 (1978)

    Article  MathSciNet  Google Scholar 

  3. Decker, W.: Monads and cohomology modules of rank 2 vector bundles. Comp. Math. 76, 7–17 (1990)

    MathSciNet  MATH  Google Scholar 

  4. Evans, G., Griffith, P.: The syzygy problem. Annals of Math. 114, 323–353 (1981)

    MathSciNet  MATH  Google Scholar 

  5. Fløystad, G.: Monads on projective spaces. Comm. Algebra 2828, 5503–5516 (2000)

    Google Scholar 

  6. Horrocks, G.: Vector bundles on the punctured spectrum of a local ring. Proc. London Math. Soc. 14, 689–713 (1964)

    MATH  Google Scholar 

  7. Horrocks, G.: Construction of bundles on P n. Les équations de Yang-Mills, A. Douady, J-L. Verdier, Astèrisque 71–72, 197–203 (1980)

  8. Horrocks, G., Mumford, D.: A rank 2 vector bundle on P 4 with 15,000 symmetries. Topology 12, 63–81 (1973)

    MATH  Google Scholar 

  9. Mohan Kumar, N., Rao, A.P.: Buchsbaum bundles on P n. J. Pure Applied Algebra 152, 195–199 (2000)

    MathSciNet  MATH  Google Scholar 

  10. Okonek, C., Spindler, H.: Mathematical instanton bundles on P 2n+1. J. Reine Angew. Math. 364, 35–50 (1986)

    MathSciNet  MATH  Google Scholar 

  11. Okonek, C., Schneider, M., Spindler, H.: Vector bundles on complex projective spaces. Birkhäuser, Boston and Basel, 1980

  12. Rao, A.P.: On self-linked curves. Duke Math. J. 49, 251–273 (1982)

    MathSciNet  MATH  Google Scholar 

  13. Rao, A.P.: A note on cohomology modules of rank two bundles. J. Alg. 86, 23–34 (1984)

    MathSciNet  MATH  Google Scholar 

  14. Spindler, H., Trautmann, G.: Special instanton bundles on P 2N+1, their geometry and their moduli. Math. Ann. 286, 559–592 (1990)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Dept. of Mathematics, Washington University, Saint Louis, MO, USA, 63130

    N. Mohan Kumar

  2. Dept. of Mathematics, Colorado State University, Fort Collins, CO, USA, 80523

    Chris Peterson

  3. Dept. of Mathematics, University of Missouri, Saint Louis, MO, USA, 63121

    A. Prabhakar Rao

Authors
  1. N. Mohan Kumar
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  2. Chris Peterson
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  3. A. Prabhakar Rao
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Correspondence to N. Mohan Kumar.

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Partially supported by NSF Grants.

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Kumar, N., Peterson, C. & Rao, A. Monads on projective spaces. manuscripta math. 112, 183–189 (2003). https://doi.org/10.1007/s00229-003-0389-x

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  • DOI: https://doi.org/10.1007/s00229-003-0389-x

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