  Associated with every quaternionic representation of a compact, connected Lie
group there is a Seiberg-Witten equation in dimension three. The moduli spaces
of solutions to these equations are typically non-compact. We construct
Kuranishi models around boundary points of a partially compactified moduli
space. The Haydys correspondence identifies such boundary points with Fueter
sections - solutions of a non-linear Dirac equation - of the bundle of
hyperk\"ahler quotients associated with the quaternionic representation. We
discuss when such a Fueter section can be deformed to a solution of the
Seiberg-Witten equation.
