  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.
