Deformation theory of the blown-up Seiberg-Witten equation in dimension three

Abstract

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.