Communications in Mathematical Physics

, Volume 55, Issue 2, pp 117–124

Instantons and algebraic geometry

  • M. F. Atiyah
  • R. S. Ward

DOI: 10.1007/BF01626514

Cite this article as:
Atiyah, M.F. & Ward, R.S. Commun.Math. Phys. (1977) 55: 117. doi:10.1007/BF01626514


Minimum action solutions for SU(2) Yang-Mills fields in Euclidean 4-space correspond, via the Penrose twistor transform, to algebraic bundles on the complex projective 3-space. These bundles in turn correspond to algebraic curves. The implication of these results for the Yang-Mills fields is described. In particular all solutions are rational and can be constructed from a series of AnsätzeAl forl≧1.

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • M. F. Atiyah
    • 1
  • R. S. Ward
    • 1
  1. 1.Mathematical InstituteUniversity of OxfordOxfordEngland

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