Confinement mechanism in various abelian projections of SU(2) lattice gluodynamics

We show that the monopole confinement mechanism in lattice gluodynamics may be a particular feature of the maximal abelian projection. We give an explicit example of the SU(2) → U(1) projection (the minimal abelian projection), in which the confinement is due to topological objects other than monopoles. We perform an analytical and numerical study of the loop expansion of the Faddeev-Popov determinant for the maximal and the minimal abelian projections, and discuss the fundamental modular region for these projections.