, Volume 55, Issue 2, pp 117-124

Instantons and algebraic geometry

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Abstract

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 AnsätzeA l forl≧1.

Communicated by R. Stora