Remarks on Nahm’s equations

Abstract

Nahm's equations are viewed in a more general context where they appear as a vector field on a moduli space of O(2)-twisted 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.

The Calogero-Françoise integrable system: algebraic geometry, Higgs fields, and the inverse problem

“…Remark 5.1. The case of d = 2 was also investigated by N. Hitchin recently in [21] in the context of Nahm's equations, where the singular Hitchin fibres are studied and non-classical conserved quantities are shown to exist.…”