Resumen de Deformation theory of the blown-up Seiberg–Witten equation in dimension three
Aleksander Doan, Thomas Walpuski
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 hyperkähler quotients associated with the quaternionic representation. We discuss when such a Fueter section can be deformed to a solution of the Seiberg–Witten equation.
