On hyper-Kahler singularities

Using a geometric realization of the SU(2)(R) symmetry and a procedure of f actorization of the gauge and SU(2)(R) charges, we study the small instanto n singularities of the Higgs branch of supersymmetric U(1)(r) gauge theorie s with eight supercharges. We derive new solutions for the moduli space of vacua preserving manifestly the eight supercharges. In particular, we obtai n an extension of the ordinary ADE singularities for hyper-Kahler manifolds and show that the classical moduli space of vacua is in general given by c otangent bundles of compact weighted projective spaces.