Deformation Theory of Periodic Monopoles (With Singularities)

Cherkis and Kapustin (Commun Math Phys 218(2): 333-371, 2001 and Commun Math Phys 234(1):1-35, 2003) introduced periodic monopoles (with singularities), i.e. monopoles on possibly singular at a finite collection of points. In this paper we show that for generic choices of parameters the moduli spaces of periodic monopoles (with singularities) with structure group are either empty or smooth hyperkahler manifolds. Furthermore, we prove an index theorem and therefore compute the dimension of the moduli spaces.