Remarks on Nahm's equations

Nigel Hitchin

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arXiv · 1708.08812

Remarks on Nahm's equations

Nigel Hitchin

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Abstract

Nahm's equations are viewed in a more general context where they appear as a vector field on a moduli space of co-Higgs bundles on the projective line. Zeros of this vector field correspond to torsion-free sheaves on a singular spectral curve which we translate in terms of a smooth curve in three-dimensional projective space. We also show how generalizations of Nahm's equations are required when the spectral curve is non-reduced and deduce the existence of non-classical conserved quantities in this situation.

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Nigel Hitchin. 2017-08-29. Remarks on Nahm's equations. https://arxiv.org/abs/1708.08812

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