  We study the full set of solutions to the ADHM equation as an affine
algebraic set, the ADHM variety. We gather the points of the ADHM variety into
subvarieties according to the dimension of the stabilizing subspace. We compute
dimension, and analyze singularity and reducibility of all of these varieties.
We also connect representations of the ADHM quiver to coherent perverse sheaves
on $\mathbb{P}^2$ in the sense of Kashiwara.
