Communications in Mathematical Physics

, Volume 59, Issue 1, pp 1–15 | Cite as

Stable vector bundles and instantons

  • Robin Hartshorne


Methods of abstract algebraic geometry are used to study rank 2 stable vector bundles on ℙ3. These bundles are then used to give self-dual solutions, called instantons, of the Yang-Mills equation onS4.


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  1. 1.
    Atiyah, M. F., Hitchin, N. J., Singer, I. M.: Deformations of instantons. Proc. Nat. Acad. Sci. USA74, 2662–2663 (1977)Google Scholar
  2. 2.
    Atiyah, M. F., Ward, R. S.: Instantons and algebraic geometry. Commun. math. Phys.55, 117–124 (1977)Google Scholar
  3. 3.
    Barth, W.: Some properties of stable rank-2 vector bundles on ℙn. Math. Ann.226, 125–150 (1977)Google Scholar
  4. 4.
    Grauert, H., Mülich, G.: Vektorbündel vom Rang 2 über demn-dimensionalen komplexprojektiven Raum. manuscripta math.16, 75–100 (1975)Google Scholar
  5. 5.
    Hartshorne, R.: Algebraic geometry. In: Graduate texts in mathematics, Vol. 52. Berlin-Heidelberg-New York: Springer 1977Google Scholar
  6. 6.
    Hartshorne, R.: Moduli of stable vector bundles on ℙ3. In preparationGoogle Scholar
  7. 7.
    Jackiw, R., Nohl, C., Rebbi, C.: Conformal properties of pseudoparticle configurations. Phys. Rev. D15, 1642–1646 (1977)Google Scholar
  8. 8.
    Maruyama, M.: Moduli of stable sheaves. I. J. Math. Kyoto Univ.17, 91–126 (1977)Google Scholar
  9. 9.
    Serre, J.-P., Géométrie et géométrie analytique. Ann. Inst. Fourier6, 1–42 (1956)Google Scholar
  10. 10.
    Wever, G.: Ph. D. Thesis, Berkeley (1977)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Robin Hartshorne
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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