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Remarks on the complex geometry of the 3-monopole

H. W. Braden·V. Z. Enolski
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Abstract

We develop the Ercolani-Sinha construction of SU(2) monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a number theoretic problem and a recently proven identity of Ramanujan provides a solution. The Ercolani-Sinha construction provides a gauge-transform of the Nahm data.

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H. W. Braden, V. Z. Enolski. 2006-01-20. Remarks on the complex geometry of the 3-monopole. https://arxiv.org/abs/math-ph/0601040

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