Monopoles and rational maps: A note on a theorem of Donaldson (Q1074937)

The SU(2)-monopoles in a gauge field theory are studied. As shown by \textit{N. J. Hitchin} [ibid. 89, 145-190 (1983; Zbl 0517.58014)], these monopoles can be obtained from solutions to the Nahm equations. The author elaborates the differential geometry associated with the spectral curve introduced in this theory by \textit{N. J. Hitchin} [ibid. 83, 579-602 (1982; Zbl 0502.58017)] and derives an interpretation of the description given by \textit{S. K. Donaldson} [ibid. 96, 387-408 (1984)] of SU(2) monopoles in terms of rational maps.