  We study the null fiber of a moment map related to dual pairs. We construct
an equivariant resolution of singularities of the null fiber, and get conormal
bundles of closed $ K_C $-orbits in the Lagrangian Grassmannian as the
categorical quotient. The conormal bundles thus obtained turn out to be a
resolution of singularities of the closure of nilpotent $ K_C $-orbits, which
is a "quotient" of the resolution of the null fiber.
